Question

If 0° < θ < 90° or 180° < θ < 270°, explain why sin 2θ is always positive.

Answer 1

Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, $\sin{2\theta}$ is always positive.

What is the trigonometric identity for sin 2θ?

It is given by:

$\sin{2\theta} = 2\sin{\theta}\cos{\theta}$

In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and $\sin{2\theta}$ is always positive.

More can be learned about trigonometric identities at brainly.com/question/24496175

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