Unit 3C Review

Front

What is the value of \( \sin^{-1}\left(-\frac{1}{2}\right) \)?

Back

The value is \( -\frac{\pi}{6} \).

Front

What are the intervals of \( \theta \) for \( [0, 2\pi) \) where \( 2\sin \theta + 1 < 0 \)?

Back

The intervals are \( (\frac{7\pi}{6}, \frac{11\pi}{6}) \cup (0, 2\pi) \).

Front

How do you simplify \( \cot x \sin x \sec^2 x \)?

Back

It simplifies to \( \sec x \).

Front

Which of the following is false: \( \sin(a+b) = \sin a \cos b - \cos a \sin b \)?

Back

This statement is false; the correct identity is \( \sin(a+b) = \sin a \cos b + \cos a \sin b \).

Front

How do you simplify \( \cos x - \cos x \sin^2 x \)?

Back

It simplifies to \( \cos^3 x \).

Front

What is the range of the inverse sine function \( \sin^{-1}(x) \)?

Back

The range is \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).

Front

What is the Pythagorean identity involving sine and cosine?

Back

The Pythagorean identity is \( \sin^2 x + \cos^2 x = 1 \).

Front

What is the definition of \( \sec x \)?

Back

The secant function is defined as \( \sec x = \frac{1}{\cos x} \).

Front

What is the relationship between sine and cosine for complementary angles?

Back

For complementary angles, \( \sin(90^\circ - x) = \cos x \).

Front

What is the double angle formula for sine?

Back

The double angle formula is \( \sin(2x) = 2\sin x \cos x \).