Simplify the expression $$\text{cot}^2x + \text{sec}^2x$$ .

The simplified expression is $$\text{csc}^2x + \tan^2x$$ .

Simplify the expression $$\frac{\text{cot}x}{\text{sec}^2x + \text{csc}^2x}$$ .

The simplified expression is $$\frac{\text{sin}x \text{cos}^2x}{\text{sec}x}$$ .

If $$\text{sin}\theta = \frac{4}{5}$$ , what is $$\text{csc}\theta$$ ?

$$\text{csc}\theta = \frac{5}{4}$$ .

What is the first strategy to simplify trigonometric expressions?

A common first strategy is to use a Pythagorean Identity.

What is the definition of tangent?

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle, or mathematically, $$\text{tan}x = \frac{\text{sin}x}{\text{cos}x}$$ .

What is the relationship between sine and cosine in a right triangle?

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, and cosine is the ratio of the length of the adjacent side to the hypotenuse.

What is the value of $$\text{sin}^2x + \text{cos}^2x$$ ?

The value is always 1, according to the Pythagorean Identity.

What is the formula for converting cotangent to sine and cosine?

$$\text{cot}x = \frac{\text{cos}x}{\text{sin}x}$$ .

What is the simplified form of $$\text{sin}^2x + \text{tan}^2x$$ ?

The simplified form is $$\text{sec}^2x$$ .

What is the relationship between cosecant and cotangent?

Cosecant and cotangent are related through the identity: $$\text{csc}^2x = 1 + \text{cot}^2x$$ .

Trigonometric Identities Practice Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Identity for sine and cosine?

Back

2.

FLASHCARD QUESTION

Front

What is the definition of cotangent?

Back

3.

FLASHCARD QUESTION

Front

What is the definition of secant?

Back

4.

FLASHCARD QUESTION

Front

What is the relationship between cosecant and sine?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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