SOLVING COMPOSITE INVERSE TRIGONOMETRIC FUNCTIONS

Find the exact value without a calculator.

Problem 1 :

Solution :

Problem 2 :

Solution :

Problem 3 :

Solution :

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :

Problem 7 :

sin(tan^-1(√3))

Solution :

Given, sin(tan^-1(√3))

= sin (π/3)

= √3/2

Problem 8 :

cos(tan^-1(-1))

Solution :

Given, cos(tan^-1(-1))

= cos(-π/4)

= cos (π/4) 

= √2/2

Problem 9 :

tan^-1(cos(π))

Solution :

Given, tan^-1(cos(π))

= tan^-1(-1)

= - π/4

= -45