SOLUTION: sin θ = 5/6

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Question 1043647: sin θ = 5/6
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
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sin θ = 5/6
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If sin%28theta%29 = 5%2F6, then

cos%28theta%29 = +/-sqrt%281-sin%5E2%28theta%29%29 = +/-sqrt%281+-+%285%2F6%29%5E2%29 = +/-sqrt%281+-+25%2F36%29 = +/-sqrt%28%2836-25%29%2F36%29 = +/-sqrt%2811%2F36%29 = +/-sqrt%2811%29%2F6.


So, by knowing sin%28theta%29, you can find the modulus (the absolute value) of cos%28theta%29.

But you can not determine the sign of cos%28theta%29.

It can be  "+" (positive)  or  "-" (negative).

To determine the sign, you need an additional info.

For example, if you know to which quadrant the angle theta belongs, then you can determine the sign of cos%28theta%29,
and then you know everything.

When you know everything for cos%28theta%29 (and sin%28theta%29, of course), then you can calculate all other trigonometric functions.