Question

Is the sqrt of 1 - sin^2 theta = cos theta true? If so, in which quadrants does angle theta terminate?

A. false
B. true; quadrants 1 and 4
C. true; quadrants 2 and 3
D. true; quadrants 1 and 3

Answer 1

Answer: The answer is option B.

Explanation:

Here,

We have,

`{ \sin }^(2) theta \: + {cos}^(2)theta = 1`

`{cos}^(2) \: theta = 1 - {sin}^(2) \: theta`

`cos \: theta = \sqrt{1 - { \sin }^(2)theta }`

So, it's true; and it lies in quadrant 1 and 4.

The reason according to the "CAST" rule cos theta is in 1st and 3rd quadrant cos theta is positive.