Question

For what value of $\theta$, $\sin^2\theta + \sin\theta + \cos^2\theta$ is equal to 2?

• A. $45^\circ$
• B. $0^\circ$
• C. $90^\circ$
• D. $30^\circ$

Answer 1

Answer: (C)

$90^\circ$

Answer 2

We know that:

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

The given expression is:

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

For this to equal 2:

$1 + \sin \theta = 2 \implies \sin \theta = 1$

The value of $\theta$ for which $\sin \theta = 1$ is $90^\circ$.