SOLUTION: 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 b

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 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 b      Log On


   

Question 1083906: 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/5))
B. cos(sin−1(x/5))
C. (1/2)sin(2sin−1(x/5))
D. sin(tan−1(x/5))
E. cos(tan−1(x/5))




1. x/sqrt(25+x^2)

2. (sqrt(25-x^2))/5

3. x/sqrt(25-x^2)

4. 5/sqrt(25+x^2)

5. x/25*(sqrt(25-x^2))
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
I will solve only one problem here, problem B). 

B. cos%28sin%28-1%29%28x%2F5%29%29  is  cos%28arcsin%28x%2F5%29%29.


   1.  Let alpha = arcsin%28x%2F5%29.

       Then alpha is the angle in Q1 (if x >= 0)  or in QVI (if x < 0).

       In any case,  sin%28alpha%29 = x%2F5 and cos%28alpha%29 is positive.


   2.  Since  sin%28alpha%29 = x%2F5, it implies that 

       cos%28alpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281+-+%28x%2F5%29%5E2%29 = sqrt%28%2825-x%5E2%29%2F25%29 = %28sqrt%2825-x%5E2%29%29%2F5.


       So, it matches with #2).

Actually, each of the rest cases is solved in a similar way.