Graph of Inverse Trigonometric Function – cos⁻¹(cosx)

Graph of Inverse Trigonometric Function – cos⁻¹(cosx)

Graph of y = cos⁻¹(cosx):

y = cos⁻¹(cosx)

cosy = cosx

General solution is y = 2nπ ± x, n ϵ Z

Now, with y ϵ [0, π]

Draw plot the graph y = cos⁻¹(cosx)

If n=0

y = 2πn ± x

= 2π(0) ± x

 = ± x

y=x and y=-x

If n=1

y = 2πn ± x

= 2π(1) ± x

 =2π ± x

y=2π+x and y=2π-x

Example: Evaluate the cos⁻¹(cos7π/6)

Solution:

cos⁻¹(cos7π/6)

=cos⁻¹(cos(2π-(5π /6))

=cos⁻¹(cos(5π /6))

(since cos⁻¹(cosx) = x,  2nπ ± x, n ϵ Z)

= 5π /6,