11/4 Simplifying Expressions Using Trigonometric Identities

Front

What is the Pythagorean identity in trigonometry?

Back

The Pythagorean identity states that for any angle \( \theta \), \( \sin^2(\theta) + \cos^2(\theta) = 1 \).

Front

What is the definition of secant?

Back

The secant of an angle \( \theta \) is defined as \( \sec(\theta) = \frac{1}{\cos(\theta)} \).

Front

What is the definition of cosecant?

Back

The cosecant of an angle \( \theta \) is defined as \( \csc(\theta) = \frac{1}{\sin(\theta)} \).

Front

What is the definition of cotangent?

Back

The cotangent of an angle \( \theta \) is defined as \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \).

Front

What is the relationship between tangent and secant?

Back

The relationship is given by the identity: \( \tan^2(\theta) + 1 = \sec^2(\theta) \).

Front

Simplify the expression: \( \frac{1 - \sin^2(\theta)}{\cos(\theta)} \)

Back

The simplified expression is \( \cos(\theta) \).

Front

Simplify the expression: \( \cot(\theta) \sec(\theta) \)

Back

The simplified expression is \( \csc(\theta) \).

Front

Simplify the expression: \( \cos^2(x)(\sec^2(x) - 1) \)

Back

The simplified expression is \( \sin^2(x) \).

Front

What is the formula for tangent in terms of sine and cosine?

Back

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

Front

What is the formula for cotangent in terms of sine and cosine?

Back

The formula is \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \).