What is the formula for $$\text{sin}(\theta - eta)$$ ?

The formula for $$\text{sin}(\theta - eta)$$ is: $$\text{sin}(\theta)\text{cos}(eta) - \text{cos}(\theta)\text{sin}(eta)$$ .

If $$\text{sin}igg(\frac{5}{13}igg)$$ and $$\text{cos}igg(\frac{4}{5}igg)$$ , how do you find $$\text{sin}(\theta - eta)$$ ?

Use the values to find $$\text{cos}(\theta)$$ and $$\text{sin}(eta)$$ , then apply the formula for $$\text{sin}(\theta - eta)$$ .

How can you simplify $$1 - \text{sin}^2(\theta)$$ ?

Using the Pythagorean identity, $$1 - \text{sin}^2(\theta) = \text{cos}^2(\theta)$$ .

How do you express $$\text{sin}(4\theta)\text{sin}(6\theta)$$ as a sum?

Using the product-to-sum formula: $$\text{sin}(4\theta)\text{sin}(6\theta) = \frac{1}{2}[\text{cos}(2\theta) - \text{cos}(10\theta)]$$ .

What is the value of $$\text{sin}^2(\theta)$$ ?

$$\text{sin}^2(\theta) = 1 - \text{cos}^2(\theta)$$ .

What is the cosine of an angle in the first quadrant?

In the first quadrant, cosine values are positive.

What is the sine of an angle in the first quadrant?

In the first quadrant, sine values are positive.

What is the significance of the unit circle in trigonometry?

The unit circle helps define the sine and cosine functions for all angles.

How do you find the exact value of trigonometric functions at specific angles?

Use known values from the unit circle or trigonometric identities.

What is the relationship between sine and cosine?

Sine and cosine are co-functions: $$\text{sin}(\theta) = \text{cos}igg(\frac{\text{π}}{2} - \thetaigg)$$ .

What is the importance of understanding trigonometric identities?

Trigonometric identities are essential for simplifying expressions and solving equations.

Lecture #22 (Exam #4 Review) - Fall 2024

Flashcard

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Mathematics

•

University

•

Practice Problem

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Hard

•

CCSS

HSF.TF.C.9, HSF.TF.C.8, HSF.TF.A.2

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the half-angle formula for cosine?

Back

Tags

CCSS.HSF.TF.C.9

FLASHCARD QUESTION

Front

Back

Use the half-angle formula: @@ ext{cos}igg(rac{5 ext{π}}{12}igg) = ext{cos}igg(rac{2 ext{π}}{3}igg) = -rac{1}{2}$$ and then apply the half-angle formula.

Tags

CCSS.HSF.TF.C.9

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

Tags

CCSS.HSF.TF.C.8

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is the product-to-sum formula for sine?

Back

Tags

CCSS.HSF.TF.C.9

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