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