Front

Define the Pythagorean Identity in trigonometry.

Back

The Pythagorean Identity states that for any angle \( \theta \), the following holds: \( \sin^2 \theta + \cos^2 \theta = 1 \).

Front

What is the definition of \( \tan \theta \)?

Back

The tangent of an angle \( \theta \) is defined as the ratio of the opposite side to the adjacent side in a right triangle, or \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).

Front

Simplify the expression: \( \frac{\csc^2 \alpha}{1 + \cot^2 \alpha} \)

Back

The simplified expression is \( 1 \).

Front

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

Back

The secant of an angle \( \theta \) is the reciprocal of the cosine: \( \sec \theta = \frac{1}{\cos \theta} \).

Front

Simplify the expression: \( \frac{-1}{\tan^2 N} + \frac{\sec^2 N}{\tan^2 N} \)

Back

The simplified expression is \( 1 \).

Front

What is the definition of \( \csc \theta \)?

Back

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

Front

Simplify the expression: \( \tan \sigma + \frac{\sec \sigma}{\csc \sigma} \)

Back

The simplified expression is \( 2 \tan \sigma \).

Front

What is the definition of \( \cot \theta \)?

Back

The cotangent of an angle \( \theta \) is defined as the ratio of the adjacent side to the opposite side in a right triangle, or \( \cot \theta = \frac{\cos \theta}{\sin \theta} \).

Front

Simplify the expression: \( \frac{1 - \cos^2 \beta}{\tan^2 \beta} \)

Back

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

Front

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

Back

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