SOLUTION: Suppose that beta is an acute angle , greater than 0 but less than 90. Compute the exact value of all of the trigonometric values of beta, given that tan beta = 3.

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose that beta is an acute angle , greater than 0 but less than 90. Compute the exact value of all of the trigonometric values of beta, given that tan beta = 3.      Log On


   

Question 1065128: Suppose that beta is an acute angle , greater than 0 but less than 90. Compute the exact value of all of the trigonometric values of beta, given that tan beta = 3.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For a right triangle with an angle measuring beta ,
tan%28beta%29= opposite leg/adjacent leg.
If we draw such a triangle with legs measuring 3 and 1 on angle beta ,
it would look like this:
x%5E2=1%5E2%2B3%5E2=1%2B3 <---> x=sqrt%2810%29 as per the Pythagorean theorem.
For that triangle, we can calculate:
sin%28beta%29=3%2Fsqrt%2810%29=3sqrt%2810%29%2F10
cos%28beta%29=1%2Fsqrt%2810%29=sqrt%2810%29%2F10
cot%28beta%29=1%2Ftan%28beta%29=1%2F3
sec%28beta%29=1%2Fcos%28beta%29%22=%221%2F%28%281%2Fsqrt%2810%29%29%29%22=%22sqrt%2810%29
csc%28beta%29=1%2Fsin%28beta%29%22=%221%2F%28%283%2Fsqrt%2810%29%29%29%22=%22sqrt%2810%29%2F3