SOLUTION: Write the first trigonometric Functions in Terms of the second for Theta in the given quadratic. CosTheta, sinTheta :Theta in quadratic 4

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Question 1117153: Write the first trigonometric Functions in Terms of the second for Theta in the given quadratic.
CosTheta, sinTheta :Theta in quadratic 4
Answer by ikleyn(52902) About Me  (Show Source):
You can put this solution on YOUR website!
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Write the first trigonometric Functions in Terms of the second for Theta in the given highlight%28cross%28quadratic%29%29 quadrant.
CosTheta, sinTheta :Theta in highlight%28cross%28quadratic%29%29 quadrant 4.
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cos%5E2%28theta%29 + sin%5E2%28theta%29 = 1  - it is Pythagorean equation, which is  ALWAYS true.


So,  cos%5E2%28theta%29 = 1+-+sin%5E2%28theta%29,  and it is  ALWAYS true,  again.


It implies that  cos%28theta%29 = +/- sqrt%281-sin%5E2%28theta%29%29,  and you must correctly determine  which of the two possible signs to select, "+" or "-".


For it, recall that cosine is positive function in QIV, while sine is negative function in QIV.


Therefore,  you must select the sign "-", and the formula, finally, takes the form


cos%28theta%29 = -sqrt%281-sin%5E2%28theta%29%29   in QIV.


It is your answer.

Solved.