Question

find cos2a; the angle a is in the 4th quadrant, and sin a= -0.75.A) 0.2800B) 0.4050C) 0.5950D) 0.3450

Answer 1

If the angle is in the 4th quadrant, its sine is negative and its cosine is positive.

First, let's calculate the cosine of a, using the trigonometrical identity below:

$\begin{gathered} \sin^2a+\cos^2a=1\\ \\ (-0.75)^2+\cos^2a=1\\ \\ 0.5625+\cos^2a=1\\ \\ \cos^2a=1-0.5625\\ \\ \cos^2a=0.4375\\ \\ \cos a=0.6614 \end{gathered}$

Now, we can use the formula below to calculate the cosine of 2a:

$\begin{gathered} \cos2a=\cos^2a-\sin^2a\\ \\ \cos2a=0.4375-0.5625\\ \\ \cos2a=-0.125 \end{gathered}$