Question

Suppose sin(A) = 1/4 Use the trig identity sin^2(A)+cos^2(A)=1 to find the cosine in quadrant II. round to ten-thousandth.0.1397-0.9682-0.85720.4630

Answer 1

To find the value f rthe cosine function we will us the identity:

$\sin^2A+\cos^2A=1$

We know that the sine of A i 1/4 then we have:

$\begin{gathered} (\frac{1}{4})^2+\cos^2A=1 \\ \cos^2A=1-\frac{1}{16} \\ \cos A=\pm\sqrt{\frac{15}{16}} \\ \cos A=\pm0.9682 \end{gathered}$

Now, we need to determine which sign to choose. Since the sinA lies in th second quadrant thismeans that tehe coosine als lies in the quadrant; furthermore, we know that the cosine is negative in the second and thirsd quadrants whichmeans that we need to use the negative sign. Therefoore:

$\cos A=-0.9682$