Compositions of Inverse Trig FunctionsTS:Explicitly assessing information and drawing conclusions.

Warm-Up:1) Use an inverse trigonometric

function to write a function for θ in terms of x.

2) Find the exact value of arctan(tan(-3.25))

.

θ

2x+23

Find the exact value of each trigonometric expression

1) arcsin(sin(-0.74))

2) tan-1(tan(3π))

3) cos(arccos(-½))

4) arctan(√3)

5) cos(arccos(-2.4))

Find the exact value of each trigonometric expression

1) sec(arcsin(3/5))

Find the exact value of each trigonometric expression

2) tan(arcsin(-3/4))

Find the exact value of each trigonometric expression

3) cot(arctan(5/8))

Solve for x.

1) sin-1(sin(x))=π/5 2) sin-

1(sin(x))=10π/5

3) cos-1(cos(x))=2

Solve for x.

1) 2cosx =-√3

2) tan(tan-1(x)) = 1/7

Find an algebraic expression that is equivalent to the expression

1) sin(arctan x) 2)

3)

4cot arctan

x

cos arcsinx h

r

2

:

3 1 13 11) arctan 2) 3) 4)

10 2 12 2

Answers

x x x

Closing Problems

2) Find sin(arcsin(.5))

3) Find csc(arctan(-12/5))

4) Write an algebraic

expression that is equivalent

to the expression

sec(arcsin(x-1))

θ

10 – x

3

1) Refer to the diagram below and write an expression for θ in terms of x