Question

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank.
A. tan(sin−1(x/4))
B. cos(sin−1(x/4))
C. (1/2)sin(2sin−1(x/4))
D. sin(tan−1(x/4))
E. cos(tan−1(x/4))

Answer 1

Answer:

Step-by-step explanation:

In each case, draw the right triangle which produces the inverse trig value. That is, label the two sides as needed, and calculate the third side.

It should be clear that

$tan(sin^{-1} x/4) = x/\sqrt{16-x^{2} }$

$sin(tan^{-1} x/4) = x/\sqrt{16+x^{2} }$

sin(2α) = 2 sinα cosα

So,

$1/2 sin(2sin^{-1} x/4) = (1/2)(x/4) * x/\sqrt{16-x^2} = x^{2} /(8\sqrt{16-x^2})$

See what you can do with the others.