![Page 1: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/1.jpg)
week 1
April 13, 2023PRECACULUS, Mathematics(2), MATH-112, McGraw Hill
Basic Sciences Department1
Outlines:- 6.1: Angles and Their Measure 6.2: Solving Right Triangles 6.3: Trigonometric Functions: A Unit Circle Approach
![Page 2: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/2.jpg)
Objectives
At the end of this lecture, the student should be able to:
Define the concept of angle and identify its sign and type . Convert from decimal degree (DD) to degree-minute-second form (DMS)
and vise versa. Convert the measure of angle from radian to degree and vise versa. Evaluate the trigonometric ratios associated with an acute angle of a right
triangle. Solve the right triangle if we given two sides or one acute angle and a side. Find the coordinates of the circular point on the unit circle or circle with
radius and find the values of all six trigonometric functions by using this point.
Evaluate the trigonometric functions to four significant digits(three using a calculator in radian mode.
prepared by : Mais Obeidat
![Page 3: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/3.jpg)
Angles and Their Measure
prepared by : Mais Obeidat
Section 6.1
![Page 4: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/4.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Degree and Radian Measure
Angles
Converting Degrees to Radians and vice versa
![Page 5: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/5.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
AnglesAn angle is formed by rotating a ray , called the initial side of the angle , around its endpoint until it coincides with a ray , called terminal side of the angle.
The vertex
Angle or angle or
![Page 6: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/6.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Sign of Angle:
Counterclockwise
Clockwise
Positive angle
Negative angle
![Page 7: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/7.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Two different angles that have the same initial and terminal sides, are called coterminal.
![Page 8: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/8.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
An angle is said to be in standard position if its vertex is at the origin and the initial side is along the positive axis.
If the terminal side of an angle in standard position along the coordinate axis, the angle is said to be a quadrantal angle.
![Page 9: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/9.jpg)
Degree and Radian Measure
Definition 1: Degree Measure
A angle formed by one complete rotation is said to have a measure of 360
degrees (36). A positive angle formed by of a complete rotation is said to have a
measure of 1 degree (1). The symbol denotes degrees
A angle formed by one complete rotationA angle formed by complete rotation 60 °
1
A angle formed by complete clockwise rotation − 90 °
Example:
![Page 10: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/10.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Types of Angles:
![Page 11: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/11.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Two positive angles are complementary if their sum is .
Two positive angles are supplementary if their sum is .
![Page 12: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/12.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Degree = 60 minute , minute = 60 second . Thus:
1 minute = degree .
Converting from decimal degree (DD) to degree-minute-second form (DMS) and vise versa:
A degree can divided using :
1 (Decimal notation ( Example : )
2 (degree-minute-second ( Example : )
1 second = minute = degree .
![Page 13: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/13.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
(A) Convert to DD form.
(B) Convert to DMS form.Solutions:
Example 1: From DMS to DD and Back
¿¿)A (
¿21 . 787°
)B ( 105° (0 . 183 ×60) ′
¿105° 10 . 98 ′
![Page 14: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/14.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Matched Problem 1:
Solutions:
(A) Convert to DD form.(B) Convert to DMS form .
¿¿)A (
¿)B( ❑°(×) ′
![Page 15: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/15.jpg)
Definition 2: Radian Measure
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
![Page 16: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/16.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
The circumference of a circle of radius is so the radian measure of a positive angle formed by one complete rotation is:
= radians
Note that, if is negative angle, its radian measure is given by .
![Page 17: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/17.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
What is the radian measure of a central angle opposite an arc of 24 meters in a circle of radius 6 meters?
Solutions:
Example 2: Computing Radian Measure
𝑠𝑟
=
=4 radians.
![Page 18: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/18.jpg)
Matched Problem 2:
Solutions:
What is the radian measure of a central angle opposite an arc of 60 feet in a circle of radius 12 feet?
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
=
………… =radians.
![Page 19: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/19.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
What is the radian measure of ?
¿2𝜋 𝑟
2¿𝜋𝑟𝑟
s=C2
θ=𝑠𝑟
𝜋
=
![Page 20: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/20.jpg)
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
Converting Degree to Radians and Vice Versa
.
.
.
![Page 21: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/21.jpg)
Solutions:
Example 3: Radian - Degree Conversions
)A (
¿𝜋
180° × (75°)
¿1 .31
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
¿5𝜋12Exact
Three significant digits
)B (
¿ 180°
𝜋× (5)
¿286 .5 °
¿ 900°
𝜋Exact
Four significant digits
![Page 22: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/22.jpg)
)C= (
Change to DD first
¿¿¿ 41 .2°
θ rad=¿
¿𝜋
180° × (41 .2°)
¿0 .72 °To two decimal places
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
![Page 23: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/23.jpg)
Matched Problem 3:
Solutions:
6.1 .Angles and Their Measure
Prepared by: Mais Obeidat
![Page 24: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/24.jpg)
Solving Right Triangles
Section 6.2
![Page 25: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/25.jpg)
Trigonometric Ratio.
Solving Right Triangles.
Evaluation of Trigonometric Ratio.
6.2. Solving Right Triangles
Prepared by : Mais Obeidat
![Page 26: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/26.jpg)
6.2. Solving Right Triangles
1¿𝛼+𝛽=90°
A right triangle is angle with one
2) Pythagorean Theorem: =
Prepared by : Mais Obeidat
Satisfied that:
it is impossible to solve the sides. If only the angles of right triangle are known,
Why?
If we are given
Two sides One acute angle and a sideT
hen
It is possible to solve the remaining three quantities. (This process is called solving the right triangle)
Trigonometric Ratios.
![Page 27: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/27.jpg)
6.2. Solving Right Triangles
Prepared by : Mais Obeidat
Therefore
If two right triangles have the same acute .
Then, the triangles are similar and ratios of corresponding sides are equal
𝑏𝑐
¿ 𝑏′
𝑐 ′
𝑎𝑐
¿ 𝑎′
𝑐′
𝑏𝑎
¿ 𝑏′
𝑎′
𝑐𝑏
¿ 𝑐′
𝑏′
𝑐𝑎
¿ 𝑐′
𝑎′
𝑎𝑏
¿ 𝑎′
𝑏′
These six ratios, the trigonometric ratios, are called sine, cosine, tangent, cosecant, secant, and cotangent.
![Page 28: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/28.jpg)
Trigonometric Ratios
6.2. Solving Right Triangles
Prepared by : Mais Obeidat
sin θ=𝑏𝑐
cos θ=𝑎𝑐
tan θ=𝑏𝑎
csc θ=𝑐𝑏
sec θ=𝑐𝑎
cot θ=𝑎𝑏
Right Triangle Ratios
sin θ=OppHyp
cos θ=AdjHyp
tan θ=OppAdj
csc θ=HypOpp
sec θ=HypAdj
cot θ=AdjOpp
HypotenuseOpposite
Adjacent
SOHCAHTOA
![Page 29: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/29.jpg)
Reciprocal Relationships
6.2. Solving Right Triangles
Prepared by : Mais Obeidat
For : csc θ
Complementary Relationships
)
¿1
sin θ sec θ¿1
cosθ cot θ¿1
tanθ
For :
)
)
)
The trigonometric ratios, cosine, cosecant , and cotangent are sometimes referred to as the cofunctions of sine , secant , and tangent, respectively.
![Page 30: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/30.jpg)
6.2. Solving Right Triangles
Prepared by : Mais Obeidat
Evaluation of Trigonometric Ratio.
sin 45°=1
√2
cos 45°=¿1
√2¿
tan 45°=1
csc 45°=√2sec 45°=√2
cot 45°=1sin 60°=√3
2
cos 60°=¿12¿
tan 60°=√3
csc 60°=¿2
√3¿
sec 60°=2cot 60°=¿
1
√3¿
Exact Values of the Trigonometric Functions( Standard angles)
How?
How? Why?
![Page 31: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/31.jpg)
Prepared by: Mais Obeidat
Evaluate to four significant digits.(A) (B) (C)
Solutions:
Example 1: Calculator Evaluation
First, make certain that the calculator is set in degree mode .
)A (
)B (
11 . 43cos (26+ 42
60)
°
¿0 .8934
6.2. Solving Right Triangles
By the calculator
)C (1
sin 34°
¿1 .788
By the calculator
![Page 32: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/32.jpg)
Prepared by: Mais Obeidat
6.2. Solving Right Triangles
Matched Problem 1:
Solutions:
Evaluate to four significant digits.
(A) (B) (C)
)A (
)B (
)C (
![Page 33: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/33.jpg)
15 minutes Break
![Page 34: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/34.jpg)
Solving Right Triangles.
Solve the right triangle with feet and
Solutions:
Example 2: Right Triangle Solution
First, draw a figure and label the parts .
Solve For : =
6.2. Solving Right Triangles
or use csc 𝛽=𝑐𝑏
α ∧𝛽 are complementary
Solve For : sin 𝛽=𝑏𝑐
sin 32 . 2°=𝑏
6 .25 𝑏=6 .25 sin 32 . 2° 𝑏=3 .33 feet
Solve For : cos 𝛽=𝑎𝑐
cos 32. 2°=𝑎
6 . 25 𝑎=6 .25 cos32 . 2° 𝑎=5 .29 feet
or use sec 𝛽=𝑐𝑎
or cos𝛼=𝑏𝑐
or cos𝛼=𝑎𝑐
![Page 35: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/35.jpg)
6.2. Solving Right Triangles
Matched Problem 1:
Solutions:
Solve the right triangle with meters. and
The inverse of sine.
If 0.4196
and ” are same
𝐨𝐫
θ=24 . 81 °To the nearest hundredth degree
𝐨𝐫θ=24 ° 49′To the nearest minute
does not mean
We use the same process with the other 5 trigonometric functions
![Page 36: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/36.jpg)
6.2. Solving Right Triangles
Solve the right triangle with cm and b= .
Solutions:
Example 3: Right Triangle Solution
First, draw a figure and label the parts .
Solve For : tan 𝛽=2 . 624 .32
or
Solve For : sin 𝛽=2 . 62𝑐
𝑐=2 .62
sin 31 . 2° 𝑐=5 . 06 𝑐𝑚
or use csc 𝛽=𝑐
2. 62
Pythagorean Theorem𝑐=√4 . 322+2 . 622=5 . 05
Solve For : =
use to solve
58° 5 0 ′
α ∧𝛽 are complementary
0.2 = [
![Page 37: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/37.jpg)
Prepared by: Mais Obeidat
6.2. Solving Right Triangles
Matched Problem 3:
Solutions:
Solve the right triangle with km and b = .
![Page 38: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/38.jpg)
Trigonometric Functions: A Unit Circle Approach
Section 6.3
Prepared by: Mais Obeidat
![Page 39: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/39.jpg)
The Wrapping Function.
6.3. Trigonometric Functions: A Unit Circle Approach
Definitions of the Trigonometric Functions.
Prepared by: Mais Obeidat
![Page 40: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/40.jpg)
6.3. Trigonometric Functions: A Unit Circle Approach
The Wrapping Function:
in standard position
The point is called a circular point
is the point of intersection of the terminal side of with unit circle + =1
denote the length of the arc opposite
radians
Prepared by: Mais Obeidat
![Page 41: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/41.jpg)
= =1=
6.3. Trigonometric Functions: A Unit Circle Approach
Prepared by: Mais Obeidat
(1,0)
(0,1)
(-1,0)
(0,-1)
(1,0)
1
1
1
𝑎=± √32
𝑊 (𝜋6 )=(√32
,12)
![Page 42: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/42.jpg)
Solutions:
Example 1: Coordinates of Circular Points
)A () =0,-1(
Find the coordinates of the following circular points .(A) (B) (C) (D) )E (
)B () = 0, 1(
)C = (,) (
))D ( -)=
)E ( ( ) =
6.3. Trigonometric Functions: A Unit Circle Approach
Prepared by: Mais Obeidat
![Page 43: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/43.jpg)
Matched Problem 1:
Solutions:
6.3. Trigonometric Functions: A Unit Circle Approach
Prepared by: Mais Obeidat
![Page 44: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/44.jpg)
Coordinates of the key circular point
Defining the Trigonometric Functions:
Definition1: Trigonometric Functions
6.3. Trigonometric Functions: A Unit Circle Approach
![Page 45: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/45.jpg)
6.3. Trigonometric Functions: A Unit Circle Approach
2) If is the point on the terminal side that lies on the circle with radius .
1) Note that the point on the unit circle
Remarks:
sin 𝑥cos 𝑥
= =1 ) , lies on the unit circle
sin 𝑥=𝑏𝑟
cos𝑥=𝑎𝑟
tan𝑥=𝑏𝑎
csc 𝑥=𝑟𝑏
,𝑏≠ 0
sec𝑥=𝑟𝑎
,𝑎≠ 0
cot 𝑥=𝑎𝑏𝑏≠ 0
Prepared by: Mais Obeidat
![Page 46: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/46.jpg)
Solutions:
Example 2: Evaluating Trigonometric Functions
)A (Identify that in unit circle or not:
Find the values of all six trigonometric functions of the angle if .(A) =( ,- )
(B) The terminal side of contains the point (- 60,- 11).
in unit circle Thus:
6.3. Trigonometric Functions: A Unit Circle Approach
𝑟=1
-
=
-
sec𝑥=1𝑎
=53
= -
Prepared by: Mais Obeidat
![Page 47: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/47.jpg)
6.3. Trigonometric Functions: A Unit Circle Approach
)B (Identify that in unit circle or not: 𝑟=√(− 60)2+ (− 11)2=61
r = 61 = = =
csc 𝑥=𝑟𝑏
=−6111
sec𝑥=𝑟𝑎
=−6160
cot 𝑥=𝑎𝑏
=6 011
Matched Problem 2:
Find the values of all six trigonometric functions of the angle if .(A) =( - , )
(B) The terminal side of contains the point (13, 84).
Prepared by: Mais Obeidat
![Page 48: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/48.jpg)
Solutions:
Example 3: Calculator Evaluation
)A ( =14.10
)B(
6.3. Trigonometric Functions: A Unit Circle Approach
Evaluate to four significant digits.(A) (B) (C) )(D) The coordinates of .
= =
)C ( = =
)D (
![Page 49: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/49.jpg)
Matched Problem 1:
Solutions:
6.3. Trigonometric Functions: A Unit Circle Approach
Evaluate to four significant digits.(A) (B) (C)
)D (The coordinates of.
Prepared by: Mais Obeidat
![Page 50: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/50.jpg)
Sample questions( Test Your Self )
Choose the correct answer for the following questions:
1. The degree measure of the angle formed by rotation is…………
2. The value of angle in decimal degree is ……………..
3. The exact value of in radian…………….
4. For the given triangle, the trigonometric function that corresponds the
ratio is………
Choose the correct answer for the following questions :
a ) b ) c ) d )
a ) b ) c ) d)
a ) b ) c) d)
a ) b- ) ) c) d)
![Page 51: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/51.jpg)
Sample Questions
5. The coordinates of the circular point is…………
6. In which quadrants must lie such that and
7. The value of )) is…………….
4. The value of is …………………
a ) b) c) d)
a) Quadrant III b) Quadrant II c) Quadrant I d) Quadrant IV
a ) b ) c) d)
a ) b ) c ) 0 d) Undefined
Prepared by: Mais Obeidat
![Page 52: Angles and their measure, Solving Right Triangle and Trigonometric Ratios](https://reader035.vdocument.in/reader035/viewer/2022062220/5583db48d8b42a423f8b4882/html5/thumbnails/52.jpg)
Home Work
Prepared by: Mais Obeidat
• P. 8, #7, 14, 19,23,25,37,41,55.• P.18 , # 10,18,21,29,35,34-42.• P.30, #9,11,29,33,39, 47, 53-56,75,81.Give all the same details as we did before .