Dec. 14 Flashcard Trig. identities. Show work where necessary!

Front

What is the identity for \( \sin(-x) \)?

Back

\( \sin(-x) = -\sin(x) \) (Odd Identity)

Front

What is the identity for \( \sin^2(-x) \)?

Back

\( \sin^2(-x) = \sin^2(x) \) (Even Identity)

Front

Simplify \( \sec(\theta) - 1 \) and \( \sec(\theta) + 1 \).

Back

\( \left(\sec(\theta) - 1\right)\left(\sec(\theta) + 1\right) = \tan^2(\theta) \)

Front

What is the definition of cotangent?

Back

\( \cot(x) = \frac{\cos(x)}{\sin(x)} \)

Front

What is the definition of cosecant?

Back

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

Front

What is the definition of secant?

Back

\( \sec(x) = \frac{1}{\cos(x)} \)

Front

What is the Pythagorean identity?

Back

\( \sin^2(x) + \cos^2(x) = 1 \)

Front

What is the identity for \( \tan(-x) \)?

Back

\( \tan(-x) = -\tan(x) \) (Odd Identity)

Front

What is the identity for \( \cos(-x) \)?

Back

\( \cos(-x) = \cos(x) \) (Even Identity)

Front

Simplify \( \sec(-\alpha) \cot(-\alpha) \sin(\alpha) \).

Back

\( \sec(-\alpha) \cot(-\alpha) \sin(\alpha) = -1 \)