Question

What is the value of cos(Tan^-1 1)?

a. 2
b.square root 2
c. 2 square root 2
d. square root 2 over 2

Answer 1

D

Explanation:

So you have the equation:
`cos(tan^-1(1))`. So let's work in order and focus on the
`tan^-1(1)` part first. The inverse of tan is essentially taking in the value of
`tan(\theta)` and returning
`\theta`. And the value of
`tan(\theta)` can be defined as
`(sin(\theta))/(cos(\theta))`. So if you look at the unit circle, you'll need to look for two values that are exactly the same. You'll notice when the angle is 45 degrees, the value of sine, and cosine are the exact same. They're both
`(\sqrt2)/(2)`. So the inverse of tan(1 degree) = 45 degrees. Now we can literally refer to the same point, because when finding the cosine of 45 degrees, we can just use the x-value. This gives a solution of
`(\sqrt2)/(2)`