Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that...
-
Upload
magdalene-malone -
Category
Documents
-
view
213 -
download
0
Transcript of Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that...
![Page 1: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/1.jpg)
Chapter 14Day 5Trig Functions of Any Angle
![Page 2: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/2.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 3: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/3.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 4: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/4.jpg)
You will need to sketch a right triangle and use the
theorem to find the length of the radius.
Pythagorean
![Page 5: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/5.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 6: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/6.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 7: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/7.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 8: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/8.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 9: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/9.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 10: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/10.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 11: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/11.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 12: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/12.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 13: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/13.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 14: Chapter 14 Day 5 Trig Functions of Any Angle. We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.](https://reader036.fdocuments.net/reader036/viewer/2022082816/56649d1b5503460f949f0ca8/html5/thumbnails/14.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