1. Quiz 13-3 1. Draw the standard position angle for 210º
2. What is the reference angle for 210º ?
3. What triangle do we need to solve? (label angle
and the length of each of the sides)
4. Is cos 210º (+) or (-) ?
5. Cos 210º = ?

2. Quiz 13-3 -x =½ 4. Is cos 210º (+) or (-) ?
1. Draw the standard position angle for 210º
2. What is the reference angle for 210º ?
3. What triangle do we need to solve? (label angle
and the length of each of the sides)
90º
5. Cos 210º = ? -x
180º 0º x
30º
30º
210º y =½
60º 1
270º

3. Inverse Trigonometric Functions
13-4
Inverse Trigonometric Functions

4. What you’ll learn about (13-4)
1. What is an Inverse trigonometric function?
How to use Inverse Trigonometric Functions
to solve for the unknown angles in a triangle
(using a calculator).
How to solve trigonometric equations using
inverse trig. functions.
4. How to evaluate inverse trigonometric
functions without using a calculator.

5. Compositions of Functions (ch-6 review)
In a composition of functions, instead of having
a number as an input value, you have another
function as an input value.
1. Your turn:

6. Compositions of Inverse Functions
The composition of inverse functions “cancels out”
each of the functions leaving:
input value = output value

7. Your turn: 2.
f(g(x) = ? 3.
f(g(x) = ?

8. Review of Section 13-1 B
Sin A = ? 17 8
Cos B = ? A C 15
Tan A = ?

9. Given: the angle and a side Find: unknown sides
Which function
would you use
to find ‘y’ ? 8 y
‘y’ = ?
25º x
Which function
would you use
to find ‘x’ ?
4. y = ?
Your turn:
5. x = ?
‘x’ = ?

10. Given: the length of the sides Find: the angles3 4 5
How do we find the angle?
If we could compose with its inverse
function, we could then have all by itself 
we would know the angle.
What is the inverse function for sine?

11. Inverse function for sine, cosine, tangent
When you compose a function with its
inverse function: output = input.
Look at the “sin” button on your calculator.
Notice the function right above the “sin” function. 3 4 5

12. Another example Use the sine ratio to find: 13 5 12 25 Your turn: 7 6.24

13. Another way to think about it:
Sine of an angle = a ratio
Inverse sine of an ratio = an angle 25 7 24

14. Your turn: 26
7. Use: 10 24
to find the measure of the
angle.

15. REMEMBER!!!
Sine (angle) = ratio
Inverse sine (ratio) = angle

16. Solving Trigonometric Equations using Inverse Functions.
Solve:
REMEMBER!!!
Inverse sine (ratio) = angle
Which triangle applies ( or ) ?
60º 1
45º 1
30º
45º
Reference angle = 45º

17. For what angles
will the sine ratio be
negative? 90
135º
45º 1
45º
180
45º
45º
45º
225º
315º
225º
315º
270

18. Solving Trigonometric Equations using Inverse Functions.
Solve:
Inverse cosine (ratio) = angle
Which triangle applies ( or ) ?
60º 1
45º 1
30º
45º
Reference angle = 30º

19. will the cosine ratio be positive? 90
For what angles
will the cosine ratio be
positive? 90
30º
150º 1
180
30º
30º
30º
30º
30º
300º
210º
300º
270

20. Your Turn: Solve: (step by step) 8. What triangle applies?
What is the reference angle?
Draw the unit circle with the 4 possible
triangles in position.
What are the angles where the tangent
ratio will be negative?

21. Word Problem:
An airplane is flying at 35,000 feet. When it is 100 miles away from the Salt Lake City airport it begins descending.
Assuming the airplane descends at the same angle for the whole distance, what is the angle of descent?
1. Draw the picture:
35,000 ft
100 miles
2. Do you need to convert any units?
Either 35,000 ft to miles or 100 miles to feet.

22. Word Problem: 1. Draw the picture: 35,000 ft 100 miles
2. Convert units
6.63 miles
100 miles
3. Set up equation.
4. Are you in angle mode?
5. Solve