What is the relationship between tangent and cotangent?

Tangent and cotangent are reciprocal functions: $$\tan x = \frac{1}{\text{cot} x}$$ and $$\text{cot} x = \frac{1}{\tan x}$$ .

What is the formula for the difference of squares?

The difference of squares formula states that $$a^2 - b^2 = (a - b)(a + b)$$ .

How do you simplify the expression (sec x - 1)(sec x + 1)?

Using the difference of squares, the expression simplifies to $$\tan^2 x$$ .

What is the identity for sin^2 x in terms of cos x?

The identity states that $$\text{sin}^2 x = 1 - \text{cos}^2 x$$ .

What is the identity for cos^2 x in terms of sin x?

The identity states that $$\text{cos}^2 x = 1 - \text{sin}^2 x$$ .

What is the identity for tan^2 x in terms of sin x and cos x?

The identity states that $$\tan^2 x = \frac{\text{sin}^2 x}{\text{cos}^2 x}$$ .

What is the sum of the squares of sine and cosine?

The sum of the squares of sine and cosine is always equal to 1: $$\text{sin}^2 x + \text{cos}^2 x = 1$$ .

What is the relationship between the angles in a right triangle and the trigonometric functions?

In a right triangle, the angles determine the ratios of the lengths of the sides, which are used to define the trigonometric functions: sine, cosine, and tangent.

5.2 Verifying Trig Identities Flashcards

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15 questions

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1.

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.

2.

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

3.

FLASHCARD QUESTION

Front

How do you verify a trigonometric identity?

Back

To verify a trigonometric identity, manipulate one side of the equation using algebraic identities and trigonometric identities until it matches the other side.

4.

FLASHCARD QUESTION

Front

What is the difference between sine and cosine?

Back

5.

FLASHCARD QUESTION

Front

What is the cotangent function?

Back

6.

FLASHCARD QUESTION

Front

What is the secant function?

Back

7.

FLASHCARD QUESTION

Front

What is the cosecant function?

Back

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