# Relating Trigonometric Functions

## Key Questions

As below

#### Explanation:

Quotient Identities. There are two quotient identities that can be used in right triangle trigonometry.

A quotient identity defines the relations for tangent and cotangent in terms of sine and cosine. ...

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Remember that the difference between an equation and an identity is that an identity will be true for ALL values.

• It means to determine if the value of a trigonometric function is positive or negative; for example, since $\sin \left(\frac{3 \pi}{2}\right) = - 1 < 0$, its sign is negative, and since $\cos \left(- \frac{\pi}{3}\right) = \frac{1}{2} > 0$, its sign is positive.

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• Pythagorean Identity

${\cos}^{2} \theta + {\sin}^{2} \theta = 1$

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• The reciprocal functions are as follows:

$\sin \left(a\right) \cdot \csc \left(a\right) = 1$

$\cos \left(a\right) \cdot \sec \left(a\right) = 1$

$\tan \left(a\right) \cdot \cot \left(a\right) = 1$