Simplify $$\frac{\text{sin} x}{\text{csc} x}$$ .

$$\frac{\text{sin} x}{\frac{1}{\text{sin} x}} = \text{sin}^2 x$$ .

What is the identity for sin(-x)?

The identity states that $$\text{sin}(-x) = -\text{sin} x$$ .

What is the identity for cos(-x)?

The identity states that $$\text{cos}(-x) = \text{cos} x$$ .

What is the identity for tan(-x)?

The identity states that $$\tan(-x) = -\tan x$$ .

Simplify $$\text{cos}^2 x - \text{sin}^2 x$$ .

This simplifies to $$\text{cos}(2x)$$ using the double angle identity.

What is the double angle identity for sine?

The double angle identity for sine states that $$\text{sin}(2x) = 2\text{sin} x \text{cos} x$$ .

What is the double angle identity for cosine?

The double angle identity for cosine states that $$\text{cos}(2x) = \text{cos}^2 x - \text{sin}^2 x$$ .

If $$\text{sin} x = -\frac{1}{3}$$ and $$\text{cos} x = \frac{2\text{sqrt}(2)}{3}$$ , find $$\tan x$$ .

$$\tan x = \frac{\text{sin} x}{\text{cos} x} = \frac{-\frac{1}{3}}{\frac{2\text{sqrt}(2)}{3}} = \frac{-\text{sqrt}(2)}{4}$$ .

Resource Library

Math

Trigonometry

Trigonometric Identities

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF.TF.C.8, HSF.TF.A.4, HSF.TF.C.9

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FLASHCARD QUESTION

Front

What is the definition of a trigonometric identity?

Back

A trigonometric identity is an equation involving trigonometric functions that is true for all values of the variable where both sides of the equation are defined.

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

What is the reciprocal identity for sine?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

What is the reciprocal identity for cosine?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

What is the reciprocal identity for tangent?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

What is the quotient identity for tangent?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

What is the quotient identity for cotangent?

Back

Tags

CCSS.HSF.TF.A.4

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