Simplify trigonometric expressions

Front

What is the formula for simplifying \( \cos^3(x) \)?

Back

The formula for simplifying \( \cos^3(x) \) is \( \cos^3(x) = \frac{1}{4}(3\cos(x) + \cos(3x)) \) using the triple angle formula.

Front

What is the identity for \( \tan^2(x) \) in terms of \( \sin(x) \) and \( \cos(x) \)?

Back

The identity for \( \tan^2(x) \) is \( \tan^2(x) = \frac{\sin^2(x)}{\cos^2(x)} \).

Front

What is the Pythagorean identity involving sine and cosine?

Back

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

Front

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

Back

\( \sin^2(x) + \cos^2(x) = 1 \) based on the Pythagorean identity.

Front

What is the double angle formula for sine?

Back

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

Front

What is the double angle formula for cosine?

Back

The double angle formula for cosine is \( \cos(2x) = \cos^2(x) - \sin^2(x) \) or \( \cos(2x) = 2\cos^2(x) - 1 \) or \( \cos(2x) = 1 - 2\sin^2(x) \).

Front

What is the relationship between \( \sin(x) \) and \( \cos(x) \) in terms of complementary angles?

Back

The relationship is \( \sin(x) = \cos(90° - x) \) and \( \cos(x) = \sin(90° - x) \).

Front

What is the formula for \( \tan(x) \) in terms of sine and cosine?

Back

The formula for \( \tan(x) \) is \( \tan(x) = \frac{\sin(x)}{\cos(x)} \).

Front

How can you express \( \sin^2(x) \) using the double angle formula?

Back

Using the double angle formula, \( \sin^2(x) = \frac{1 - \cos(2x)}{2} \).

Front

What is the formula for simplifying \( \cos^2(x) \)?

Back

The formula for simplifying \( \cos^2(x) \) is \( \cos^2(x) = \frac{1 + \cos(2x)}{2} \).