Question

Is square root 1 minus sine squared theta = cos Θ true? If so, in which quadrants does angle Θ terminate?

Answer 1

√(1-sin^2(theta))= cos(theta)
If we square the equation, than we have:
1-sin^2(theta) = cos^2(theta)
sin^2(theta) + cos^2(theta) = 1 which is TRUE.
The another answer is in the quadrants where sine is positive: I, IV
That leads to the answer: B

Answer 2

Answer:

True; quadrants I & IV

Step-by-step explanation:

We know the relation between sine and cosine function which is given by

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

Let us solve this equation for cosine function.

$\cos^2 \theta = 1-\sin^2 \theta$

Take square root both sides. When ever we take square root we need to write the solution in plus minus form

$\sqrt{\cos^2 \theta}=\pm\sqrt{1-\sin^2 \theta}$

$\cos \theta=\pm\sqrt{1-\sin^2 \theta}$

$\cos \theta=-\sqrt{1-\sin^2 \theta}, \sqrt{1-\sin^2 \theta}$

If Θ is in quadrants I and IV then the value will be positive and if Θ is in II and III quadrant then the value is negative.

Hence, if Θ is in quadrants I & IV, then we have

$\cos \theta=\sqrt{1-\sin^2 \theta}$

Thus, the correct option is: True; quadrants I & IV