chapter 12-trigonometry 1 mdis

7/29/2019 Chapter 12-Trigonometry 1 MDIS

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Chapter 12 : Trigonometry 1

1. Basic Concepts:Angles in Radians Examples

Write the following angles in radians.

Write the following angles in degrees.


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in

degrees

0 30 45 60 90

in

radians

0

sin

cos

tan

1. Must memorize the table.2. The table can be extended to other

special angles > 90 . ( Will be in latersection )


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Example 1 :

Solution :


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4 Quadrants

Positive angles are meastured anti-clockwise from the positivex-axis

** can have angles > 360 ?

Negative angles are meastured clockwisefrom the positivex-axis


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Trigonometric ratios for angle > 90, we need to use the 4 quadrants.

Trigonometric ratios for or Examples



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Must memorize :

In degrees :

In radians :


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Example 2 :

Solution :


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Must Memorize the following formulae :

Further Trigonometric Ratio

Complimentary Angles Formula :

Supplementary Angles Formula :

Negative Angles Formula :


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Example 3 :

Solution :


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Basic angle, in the 1st Quadrant /:

Basic angle, in the 2n Quadrant /:

Basic angle, in the 3r Quadrant /:

Basic angle, in the 4t Quadrant /:


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Must memorize :

In degrees :

In radians :


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Example 4 :

Solution :


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Example 5 :

Solution :


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Example 6 :

Solution :


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2. Solving Basic Trigonometric Ratios Equation:

* If 3600 is used, is in degrees

If 20 is used,is radians

**

** kcan be any real numbers

** 3600 is range of the value that

can exist.

Examples

Solve the following

(a) 5.0sin where 3600 (b) 2 1cos where 1800 (c) 2 12tan x where 180180 (d) 2 1

42sin

x where 20

Special Notations of trigonometry ratioswith powers

Discussions

Forn is a positive real numbers ,

Note :

But ,


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Steps to Solve

when is in degrees or radians

Discussions

1. Find the basic angle, for

** Ifis degree / radian, must change thecalculator to degree / radian mode

2. andASTC to identify which quadrants does lies.

3. Using the basic angle , find the values ofineach of the quadrant that lies.

** Must check that the value ofis within

or

Solve 5.0sin where 3600


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Example 7 :

Solution :


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Example 8 :

Solution :


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Example 9 :

Solution :


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Example 10 :

Solution :


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Example 11 :

Solution :


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Example 12 :

Solution :


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Simple Trigonometry Identities Examples

ConsiderExample : Simplify

2sin

cos1cos1

Example : Simplify tansectansec

Example : Simplify xx

x

sin1sin1

cosec12


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Example 13 :

Solution :


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Example 14 :

Solution :


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Example 15 :

Solution :


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Example 16 :

Solution :


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Worksheet : Trigonometry 1


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Answers :


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chapter 12-trigonometry 1 mdis

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