# Given that sin t =(1/4) and that P(t) is a point in the second quadrant, what is the cos of t?

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Mar 8, 2018

$\cos \left(t\right) = - \frac{\sqrt{15}}{4}$

#### Explanation:

Given $\sin \left(t\right) = \frac{1}{4}$

Use the identity:

$\cos \left(t\right) = \pm \sqrt{1 - {\sin}^{2} \left(t\right)}$

We are told that $t$ is in the second quadrant and we know that the cosine function is negative in the second quadrant, therefore, we chose the negative value for the identity:

$\cos \left(t\right) = - \sqrt{1 - {\sin}^{2} \left(t\right)}$

Substitute ${\sin}^{2} \left(t\right) = {\left(\frac{1}{4}\right)}^{2}$:

$\cos \left(t\right) = - \sqrt{1 - {\left(\frac{1}{4}\right)}^{2}}$

$\cos \left(t\right) = - \sqrt{\frac{15}{16}}$

$\cos \left(t\right) = - \frac{\sqrt{15}}{4}$

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