SOLUTION: What is the value of sin α if tan α = -5/9 and sec α > 0?

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Question 979151: What is the value of sin α if tan α = -5/9 and sec α > 0?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since tangent is negative and secant is positive, this forces the angle to be in quadrant 4.

Draw a right triangle in this quadrant. Make the opposite leg (from the angle) 9 units long. Make the adjacent leg 5 units long. Use the pythagorean theorem to solve 5%5E2%2B9%5E2+=+c%5E2 to get c+=+sqrt%28106%29

So the sine of that angle is opposite%2Fhypotenuse+=+-9%2F%28sqrt%28106%29%29

Notes:

1) You can rationalize the denominator, but some books allow you to have that result. If you have to rationalize the denominator, then you should get %28-9%2Asqrt%28106%29%29%2F106

2) Sine is negative in Q4.