Trig Identities Practice

Front

What is the identity for \( \sec^2 \theta \)?

Back

\( \sec^2 \theta = 1 + \tan^2 \theta \) (Pythagorean Identity)

Front

Simplify \( \left(\sec\theta-1\right)\left(\sec\theta+1\right) \)

Back

\( \tan^2\theta \)

Front

What is \( \csc \theta \) in terms of \( \sin \theta \)?

Back

\( \csc \theta = \frac{1}{\sin \theta} \)

Front

If \( \sin \theta = \frac{4}{5} \), find \( \csc \theta \).

Back

\( \csc \theta = \frac{5}{4} \)

Front

What is the double angle formula for cosine?

Back

\( \cos(2x) = \cos^2(x) - \sin^2(x) \)

Front

If \( \sin x = \frac{12}{13} \) and \( \frac{\pi}{2} < x < \pi \), find \( \cos(2x) \).

Back

\( \cos(2x) = -\frac{119}{169} \)

Front

Simplify \( \sec \theta \cot \theta \sin \theta \)

Back

\( 1 \)

Front

What is the relationship between \( \tan \theta \) and \( \sin \theta \) and \( \cos \theta \)?

Back

\( \tan \theta = \frac{\sin \theta}{\cos \theta} \)

Front

What is the identity for \( \cot^2 \theta \)?

Back

\( \cot^2 \theta = \csc^2 \theta - 1 \) (Pythagorean Identity)

Front

What is the value of \( \tan(90^{\circ}) \)?

Back

Undefined (as \( \cos(90^{\circ}) = 0 \))