![Page 1: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/1.jpg)
Chapter 14Day 5Trig Functions of Any Angle
![Page 2: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/2.jpg)
The of a circle is a portion of the of a
circle.
arccircumference
![Page 3: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/3.jpg)
In the unit circle, the arc length is equal to the measure of the angle formed by the initial side and the terminal side.
However, in a circle that has a radius other than 1, this isn’t the case.
The arc length of a circle is the following:
Where θ is the measure of the angle in
, and r is the length of the .
radian
radiansradius
arc length r
![Page 4: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/4.jpg)
Find the length of the arc on a circle with the given radius that is intercepted by the central angle of the given measure.
1. 2.8 cm; 330º
2. 630 mm; 56
![Page 5: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/5.jpg)
Find the radius of a circle in which the arc of given length is intercepted by the given central angle.
3. Arc AB: 35π cm; θ=315º
4. Arc AB:
259
in.; 300o
![Page 6: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/6.jpg)
We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit circle. We just need to adjust the trig ratio for the different .
When given the coordinates of a point on the terminal side of an angle, θ, in standard position, we can evaluate the six trig functions using these rules:
radius
![Page 7: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/7.jpg)
cosθ = sec θ =
sin θ = csc θ =
tan θ = cot θ =
Where x is the of the point, y is the of the point, and r is the
of the circle.
x-coordinate
y-coordinateradius
![Page 8: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/8.jpg)
You will need to sketch a right triangle and use the
theorem to find the length of the radius.
Pythagorean
![Page 9: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/9.jpg)
Find the value of the six trigonometric functions of the angle θ whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so.
5. 5, 12
![Page 10: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/10.jpg)
Find the value of the six trigonometric functions of the angle θ whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so.
6. 2, 2
![Page 11: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/11.jpg)
Find the value of the six trigonometric functions of the angle θ whose terminal side in standard position passes through the given point. If the function is not defined for the angle, state so.
Try these on your own!
7.
8.
4,2 3
0,3
![Page 12: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/12.jpg)
We can also use the same rules when given the value of one trig function and the quadrant that it lies in. Use the given to get x, y, and/or r and then use the Pythagorean theorem to find the missing value.
![Page 13: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/13.jpg)
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value.
9. sin 5
13; Q III
![Page 14: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/14.jpg)
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value.
10. cos 15
17; Q I
![Page 15: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/15.jpg)
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value.
11. csc 2
3;Q IV
![Page 16: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/16.jpg)
Find the values of the other five trigonometric functions of the angle in the given quadrant having the given function value.
12. sec 13
2; Q IV
![Page 17: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/17.jpg)
Find and if is the point where the terminal side of in standard position intersects the unit circle and x and y satisfy the given conditions.
13.
sin cos R x, y
4x 3y, x 0
![Page 18: Chapter 14 Day 5 Trig Functions of Any Angle. The of a circle is a portion of the of a circle. arc circumference](https://reader036.vdocument.in/reader036/viewer/2022083006/56649f305503460f94c4ab5b/html5/thumbnails/18.jpg)
Find and if is the point where the terminal side of in standard position intersects the unit circle and x and y satisfy the given conditions.
14.
sin cos R x, y
y x 3, x 0