If $$\text{sin}(x) = \frac{1}{2}$$ , what is $$\text{sin}(2x)$$ ?

$$\text{sin}(2x) = 2\text{sin}(x)\text{cos}(x) = 2 \times \frac{1}{2} \times \frac{\text{\text{sqrt}}{3}}{2} = \frac{\text{\text{sqrt}}{3}}{2}$$

If $$\text{cos}(\theta) = \frac{4}{5}$$ , find $$\text{cos}(2\theta)$$ .

$$\text{cos}(2\theta) = 2\text{cos}^2(\theta) - 1 = 2 \times \frac{16}{25} - 1 = \frac{7}{25}$$

What is $$\text{sin}(6x)$$ in terms of $$\text{sin}(3x)$$ and $$\text{cos}(3x)$$ ?

$$\text{sin}(6x) = 2\text{sin}(3x)\text{cos}(3x)$$

What is $$\text{cos}(10x)$$ in terms of $$\text{cos}(5x)$$ and $$\text{sin}(5x)$$ ?

$$\text{cos}(10x) = \text{cos}^2(5x) - \text{sin}^2(5x)$$

If $$\text{sin}(x) = \frac{1}{2}$$ , what is $$\text{cos}(2x)$$ ?

$$\text{cos}(2x) = 1 - 2\text{sin}^2(x) = 1 - 2 \times \frac{1}{4} = \frac{1}{2}$$

What is the double angle identity for tangent?

$$\text{tan}(2\theta) = \frac{2\text{tan}(\theta)}{1 - \text{tan}^2(\theta)}$$

If $$\text{sin}(x) = \frac{1}{2}$$ , what is $$\text{tan}(2x)$$ ?

$$\text{tan}(2x) = \frac{2\text{tan}(x)}{1 - \text{tan}^2(x)} = \frac{2 \times \frac{1}{\text{\text{sqrt}}{3}}}{1 - \frac{1}{3}} = \frac{2\text{\text{sqrt}}{3}}{2/3} = 3\text{\text{sqrt}}{3}$$

What is the significance of the double angle formulas in trigonometry?

They allow for the simplification of expressions and the calculation of trigonometric values for double angles.

Trig: Double Angles Flashcards

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1.

FLASHCARD QUESTION

Front

What is the double angle formula for sine?

Back

Tags

CCSS.HSF.TF.C.9

2.

FLASHCARD QUESTION

Front

What is the double angle formula for cosine?

Back

Tags

CCSS.HSF.TF.C.9

3.

FLASHCARD QUESTION

Front

What is the double angle formula for tangent?

Back

Tags

CCSS.HSF.TF.C.9

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

6.

FLASHCARD QUESTION

Front

What is the relationship between sine and cosine in the double angle formulas?

Back

Tags

CCSS.HSF.TF.C.9

7.

FLASHCARD QUESTION

Front

Back

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CCSS.HSF.TF.C.9

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