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

The Correct Option is C

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 \(90^\circ\).