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Sin theta = 3/4, what are the values of cos theta and tan theta?

User Aizaz
by
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1 Answer

4 votes

Answer:


\displaystyle \cos(\theta) = (√(7))/(4).


\displaystyle \tan(\theta) = (3√(7))/(7).

Explanation:

By the Pythagorean identity, for any given angle
\theta,
\sin^(2)(\theta) + \cos^(2)(\theta) = 1.

Given that
\displaystyle \sin(\theta) = 3/4, solve this equation for
\cos(\theta).


(\sin(\theta))^(2) + (\cos(\theta))^(2) = 1.


\displaystyle \left((3)/(4)\right)^(2) + (\cos(\theta))^(2) = 1.


\begin{aligned} \cos(\theta) &= \sqrt{1 - (9)/(16)} \\ &= \sqrt{(7)/(16)} \\ &= (√(7))/(4) \end{aligned}.

The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:


\begin{aligned} \tan(\theta) &= (\sin(\theta))/(\cos(\theta)) \\ &= (3/4)/(√(7)/4) \\ &= (3)/(√(7)) \\ &= (3√(7))/(7)\end{aligned}.

User Ian Brown
by
8.6k points

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