Double and Half Angle Identities

HPC 5.5

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Day 1

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Double Angle Identities

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Cos 2a = Cos (a + a)

Use the Sum formula for cosine to rewrite cos(a + a) in terms of sine and cosine.

Multiple Select

Cos 2a = ?

• $$\cos^2a-\sin^2a$$

• $$2\cos^2a-1$$

• $$1-2\sin^2a$$

Multiple Select

Solve: $$\sin2x-\sin x=0$$  

• 0

• $$\pi$$  

• $$\frac{\pi}{3}$$  

• $$\frac{2\pi}{3}$$  

• $$\frac{5\pi}{3}$$  

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​tan 2Θ

Multiple Select

$$\sin\ 2u$$
Evaluate, where u is in the first quadrant:

$$Sin\ u\ =\ \frac{3}{5}$$  

• $$\frac{24}{5}$$  

• $$\frac{24}{25}$$  

• $$\frac{24}{50}$$  

• $$\frac{12}{25}$$  

Multiple Select

$$\sin\ u=\frac{3}{5}$$ Evaluate, where u is in the first quadrant: $$\tan\ 2u$$  

• $$\frac{24}{7}$$  

• $$\frac{7}{24}$$  

• $$\frac{24}{50}$$  

• $$\frac{3}{4}$$  

Multiple Select

$$\sin\ u=\frac{3}{5}$$ Evaluate, where u is in the first quadrant: $$\cot\ 2u$$  

• $$\frac{24}{7}$$  

• $$\frac{7}{24}$$  

• $$\frac{24}{50}$$  

• $$\frac{3}{4}$$  

Homework

• Page 390

• # 7, 12, 14, 15, 21, 22, 25