SOLUTION: When x is in quadrant 1 and cosx=1/3, what is sinx?

Algebra ->  Trigonometry-basics -> SOLUTION: When x is in quadrant 1 and cosx=1/3, what is sinx?      Log On


   

Question 1156023: When x is in quadrant 1 and cosx=1/3, what is sinx?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


cos%28x%29+=+1%2F3

cos%5E2%28x%29+=+%281%2F3%29%5E2 Square both sides

cos%5E2%28x%29+=+1%2F9

sin%5E2%28x%29%2Bcos%5E2%28x%29+=+1+ Pythagorean Trig Identity

sin%5E2%28x%29+=+1-cos%5E2%28x%29+ Subtract cos^2(x) from both sides

sin%5E2%28x%29+=+1-1%2F9 Substitution

sin%5E2%28x%29+=+9%2F9-1%2F9

sin%5E2%28x%29+=+%289-1%29%2F9

sin%5E2%28x%29+=+8%2F9

sin%28x%29+=+sqrt%288%2F9%29 Apply the square root to both sides. Sine is positive in quadrant 1

sin%28x%29+=+sqrt%288%29%2Fsqrt%289%29

sin%28x%29+=+sqrt%288%29%2F3 This is one way to write the answer

sin%28x%29+=+sqrt%284%2A2%29%2F3

sin%28x%29+=+sqrt%284%29%2Asqrt%282%29%2F3

sin%28x%29+=+2%2Asqrt%282%29%2F3 This is another equivalent way to write the answer