Simplifying Trigonometric Identities

Front

What is the Pythagorean identity in trigonometry?

Back

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

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Back

-1

Front

What is the relationship between secant and cosine?

Back

Secant is the reciprocal of cosine: \( \sec x = \frac{1}{\cos x} \).

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Back

1

Front

What is the definition of tangent in terms of sine and cosine?

Back

Tangent is defined as the ratio of sine to cosine: \( \tan x = \frac{\sin x}{\cos x} \).

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Back

1 (This is a form of the Pythagorean identity).

Front

What is the definition of cotangent?

Back

Cotangent is the reciprocal of tangent: \( \cot x = \frac{1}{\tan x} = \frac{\cos x}{\sin x} \).

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Back

\sec^2 x (This is another form of the Pythagorean identity).

Front

What is the co-function identity for sine and cosine?

Back

The co-function identity states that \( \sin(90^\circ - \theta) = \cos \theta \).

Front

What is the co-function identity for tangent and cotangent?

Back

The co-function identity states that \( \tan(90^\circ - \theta) = \cot \theta \).