If $$\text{sin}(x) = \frac{12}{13}$$ and $$\frac{\text{pi}}{2}

$$\text{tan}(2x) = \frac{120}{119}$$

If $$\text{csc}(\theta) = -\text{sqrt}(26)$$ and $$270^\text{o}

$$\text{tan}igg(\frac{\theta}{2}igg) = -\text{sqrt}(26) + 5$$

If $$\text{cos}(\theta) = \frac{4}{5}$$ and $$\frac{3\text{pi}}{2}

$$\text{sin}(2\theta) = -\frac{24}{25}$$

What is the relationship between sine and cosine in the context of double-angle identities?

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

What is the relationship between tangent and sine/cosine?

$$\text{tan}(x) = \frac{\text{sin}(x)}{\text{cos}(x)}$$

State the Pythagorean Identity for sine and cosine.

$$\text{sin}^2(x) + \text{cos}^2(x) = 1$$

What is the formula for Tangent of Half Angle?

$$\text{tan}igg(\frac{x}{2}igg) = \frac{1 - \text{cos}(x)}{\text{sin}(x)} = \frac{\text{sin}(x)}{1 + \text{cos}(x)}$$

Explain how to derive the Double-Angle Identity for Sine from the Sum of Angles Identity.

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

HIM 3 Double-Angle and Half Angle Identities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define the Double-Angle Identity for Sine.

Back

2.

FLASHCARD QUESTION

Front

Define the Double-Angle Identity for Cosine.

Back

3.

FLASHCARD QUESTION

Front

Define the Half-Angle Identity for Sine.

Back

4.

FLASHCARD QUESTION

Front

Define the Half-Angle Identity for Cosine.

Back

5.

FLASHCARD QUESTION

Front

What is the formula for Tangent of Double Angle?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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