SOLUTION: if sin theta is 3/5, and theta is in the first quadrant , find the other trigonomteric functions.

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Question 1014679: if sin theta is 3/5, and theta is in the first quadrant , find the other trigonomteric functions.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
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if sin theta is 3/5, and theta is in the first quadrant , find the other trigonomteric functions.
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sin%28theta%29 = 3%2F5.


Then cos%28theta%29 = sqrt%281+-+sin%5E2%28theta%29%29 = sqrt%281+-+%283%2F5%29%5E2%29 = sqrt%281+-+%289%2F25%29%29 = sqrt%28%2825-9%29%2F25%29 = sqrt%2816%2F25%29 = 4%2F5.


tan(theta) = sin%28theta%29%2Fcos%28theta%29 = %28%283%2F5%29%29%2F%28%284%2F5%29%29 = 3%2F4.


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

if sin theta is 3/5, and theta is in the first quadrant , find the other trigonomteric functions.
Note that all ratios will be positive since theta is in the 1st quadrant

With sin+%28theta%29+=+3%2F5, it follows that: y (opposite) = 3, and r (hypotenuse) = 5. This represents a 3-4-5 right triangle, and so, x (adjacent) MUST BE 4.

Therefore the other 5 trig ratios are:

1)  highlight_green%28csc+%28theta%29+=+H%2FO+=+5%2F3%29  

2)  highlight_green%28cos+%28theta%29+=+A%2FH+=+4%2F5%29          3)  highlight_green%28sec+%28theta%29+=+H%2FA+=+5%2F4%29

4)  highlight_green%28tan+%28theta%29+=+O%2FA+=+3%2F4%29          5)  highlight_green%28cot+%28theta%29+=+A%2FO+=+4%2F3%29