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Q. 5.2.7

Using the fundamental identity

Find cos α, given that sin α = 3/5 and α is an angle in quadrant II.

Verified Solution

Use the fundamental identity $\sin ^{2} \alpha+\cos ^{2} \alpha=1$ to find cos α:

$\left(\frac{3}{5}\right)^{2}+\cos ^{2} \alpha=1$             Replace sina with 3/5.

$\cos ^{2} \alpha=\frac{16}{25}$                       $1-\frac{9}{25}=\frac{16}{25}$.

$\cos \alpha=\pm \sqrt{\frac{16}{25}}=\pm \frac{4}{5}$

Since cos α < 0 for any α in quadrant II, we choose the negative sign and get cos α = -4/5.