SOLUTION: Could you please help me solve this problem. Can you also show the steps, thank you. tan[(cos^(-1))(1/sqrt(17))]

Algebra ->  Trigonometry-basics -> SOLUTION: Could you please help me solve this problem. Can you also show the steps, thank you. tan[(cos^(-1))(1/sqrt(17))]      Log On


   

Question 918222: Could you please help me solve this problem. Can you also show the steps, thank you.
tan[(cos^(-1))(1/sqrt(17))]
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Tan%28Cos%5E%28-1%29expr%28%281%2Fsqrt%2817%29%29%5E%22%22%29%29

Since 1%2Fsqrt%2817%29 is positive, its inverse cosine is a positive
angle between 0 and pi%2F2 in radians or between 0° and 90°, in degrees.
Therefore the tangent will be positive.

let theta=Cos%5E%28-1%29expr%28%281%2Fsqrt%2817%29%29%5E%22%22%29

Then the problem becomes to find Tan%28theta%29

Take the cosine of both sides of 

theta=Cos%5E%28-1%29expr%28%281%2Fsqrt%2817%29%29%5E%22%22%29

cos%28theta%29=1%2Fsqrt%2817%29

cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1

sin%5E2%28theta%29=1-cos%5E2%28theta%29

Substituting:

sin%5E2%28theta%29=1-%281%2Fsqrt%2817%29%29%5E2

sin%5E2%28theta%29=1-1%2F17

sin%5E2%28theta%29=17%2F17-1%2F17

sin%5E2%28theta%29=16%2F17

sin%28theta%29=%22%22+%2B-+sqrt%2816%2F17%29

sin%28theta%29=+%22%22+%2B-+4%2Fsqrt%2817%29

Tan%28theta%29=sin%28theta%29%2Fcos%28theta%29

Tan%28theta%29=%28%22%22+%2B-+4%2Fsqrt%2817%29%29%2F%281%2Fsqrt%2817%29%29

Since we know that the answer is positive we can ignore the ±.



Edwin