Find the exact value of $$\text{cos}(20)\text{cos}(40) - \text{sin}(20)\text{sin}(40)$$ .

The exact value is $$\frac{1}{2}$$ .

Which identity represents $$\text{cos}(A + B)$$ ?

$$\text{cos}(A + B) = \text{cos}(A)\text{cos}(B) - \text{sin}(A)\text{sin}(B)$$ .

Write $$\text{cos}(175)\text{cos}(55) + \text{sin}(175)\text{sin}(55)$$ as a single cosine function.

It can be written as $$\text{cos}(120)$$ .

What is the equivalent of $$\tan(A - B)$$ ?

$$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$$ .

What is the value of $$\frac{\tan 45^\text{o} + \tan 30^\text{o}}{1 - \tan 45^\text{o} \tan 30^\text{o}}$$ ?

The value is $$\tan 75^\text{o}$$ .

What is the relationship between sine and cosine in the context of the Sum Identity?

In the Sum Identity, sine and cosine are combined to express the sine or cosine of a sum of angles.

How can the Sum and Difference Identities be used in problem-solving?

They can simplify expressions involving trigonometric functions and help find exact values.

What is the significance of the angle measures in the identities?

The angle measures (A and B) can be any angles, allowing the identities to be applied broadly in trigonometry.

What is the importance of understanding Sum and Difference Identities in trigonometry?

They are fundamental for solving complex trigonometric equations and understanding the behavior of trigonometric functions.

Sum and Difference Identities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Sum Identity for Cosine?

Back

2.

FLASHCARD QUESTION

Front

What is the Difference Identity for Cosine?

Back

3.

FLASHCARD QUESTION

Front

What is the Sum Identity for Sine?

Back

4.

FLASHCARD QUESTION

Front

What is the Difference Identity for Sine?

Back

5.

FLASHCARD QUESTION

Front

What is the formula for Tangent of a Sum?

Back

6.

FLASHCARD QUESTION

Front

What is the formula for Tangent of a Difference?

Back

7.

FLASHCARD QUESTION

Front

Back

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