SOLUTION: Let (7,-5) be a point on the terminal side of theta. Find csc of theta, sin of theta and tan of theta?

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Question 614437: Let (7,-5) be a point on the terminal side of theta. Find csc of theta, sin of theta and tan of theta?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
One way to do this is by using the coordinates directly. In order to do it this way, you have to know how the "opposite", "adjacent" and "hypotenuse" of the various ratios translate into coordinates:
  • Opposite = y
  • Adjacent = x
  • Hypotenuse = r. We can use the Pythagorean Theorem to express r in terms of x and y:
    x%5E2+%2B+y%5E2+=+r%5E2
    sqrt%28x%5E2+%2B+y%5E2%29+=+r (Always use a positive r.) So:
    Hypotenuse = sqrt%28x%5E2%2By%5E2%29
We are no ready to requested functions:

sin%28theta%29+=+1%2Fcsc%28theta%29+=+5%2Fsqrt%2874%29
tan%28theta%29+=+opposite%2Fadjacent+=+y%2Fx+=+5%2F%28-7%29+=+-5%2F7

P.S. You may want/need to rationalize the denominator of sin%28theta%29.