Precalculus 4.7 Inverse Trigonometric Functions 1

Bellwork

Use your unit circle to find the possible values of

Keep the unit circle handy for reference during today’s notes

sin 1

2cos

3

2tan 1

4.7 Inverse Trig FunctionsObjectives:

Identify the domain and range of the inverse trigonometric functions

Use inverse trig functions to find angles

Evaluate combinations of trig functions

Precalculus 4.7 Inverse Trigonometric Functions 3

Calculator Practice

· Use your calculator to evaluate the three problems from bellwork

· Do the calculator answers match your answers from the unit circle?

sin 1

2cos

3

2tan 1

sin 1 1

2

cos 1 3

2

tan 1 1

Precalculus 4.7 Inverse Trigonometric Functions 4

Inverse Sine Function: Arcsin

The inverse sine graph

Precalculus 4.7 Inverse Trigonometric Functions 5

Precalculus 4.7 Inverse Trigonometric Functions 6

Inverse Cosine Function: Arccos

Precalculus 4.7 Inverse Trigonometric Functions 7

Example

1 2Find the exact value of cos .

2

1Find the exact value of sin 0.

1 3Find the exact value of tan .

3

Precalculus 4.7 Inverse Trigonometric Functions 8

Example

· Find the exact value.

arccos2

2arccos( 1)

arctan0

arctan( 1)

Precalculus 4.7 Inverse Trigonometric Functions 9

Example

· Find the exact value (when possible)

tan(arctan( 5))

arcsin sin53

cos(cos 1 )

Precalculus 4.7 Inverse Trigonometric Functions 10

Example

· Find the exact value of

tan arccos2

3

x

y

Precalculus 4.7 Inverse Trigonometric Functions 11

Example

· Find the exact value of

cos arcsin 3

5

x

y

Precalculus 4.7 Inverse Trigonometric Functions 12

Assignments

· Classwork (You Try)· Label assignment CW 4.7· Pg. 351: #5-15 odd, 19-23 odd, 27-53 odd, 71

· Homework· Label assignment HW 4.7· Pg. 351: #24, 26,32, 48, 56 (full write-up),

72, 80-83 all