Transcript Compositions of Inverse Trig Functions

Compositions of Inverse Trig Functions
TS:Explicitly assessing information and drawing conclusions.
Warm-Up:
1) Use an inverse trigonometric
function to write a function for θ in terms of x.
2x+2
3
θ
2) Find the exact value of arctan(tan(-3.25))
.
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
3) cos-1(cos(x))=2
2) sin-1(sin(x))=10π/5
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) cot  arctan 4 



3) cos  arcsin x  h 


r 

x
Closing Problems
1) Refer to the diagram
below and write an
2) Find sin(arcsin(.5))
expression for θ in terms
of x
3) Find csc(arctan(-12/5))
θ
10 – x
3
Answers :
4) Write an algebraic
expression that is equivalent
to the expression
sec(arcsin(x-1))
1
 3 
1)  arctan 
 2)
2
 10  x 
13
3) 
12
4)
1
2 x  x2