Free Printable Review: Half Angle, Sum to Product & Product to Sum

1.

Use the Product to Sum Identities to rewrite the following: $\cos2y\ \cdot\sin\ 5y$

a)

$\frac{1}{2}\sin7y+\frac{1}{2}\sin3y$

b)

$\frac{1}{2}\sin7y+\sin3y$

c)

$\frac{1}{2}\sin7y-\frac{1}{2}\sin3y$

d)

$\frac{1}{2}\sin7y-\sin3y$

2.

Use the Product to Sum Identities to rewrite the following: $\sin5B\sin B$

a)

$\frac{\cos4B-\cos6B}{2}$

b)

$\frac{\sin4B+\cos6B}{2}$

c)

$\frac{\sin6B+\sin4B}{2}$

d)

$\frac{\cos4B-\sin6B}{2}$

3.

Use the Product to Sum Identities to rewrite the following: $\cos57\degree\sin55\degree$

a)

$\frac{\cos112\degree-\cos2\degree}{2}$

b)

$\frac{\sin112\degree-\sin2\degree}{2}$

c)

$\frac{\sin2\degree+\sin112\degree}{2}$

d)

$\frac{\sin112\degree-\cos\ 2\degree}{2}$

4.

Use the Sum to Product Identities to rewrite the following: $\cos5A-\cos A$

a)

$-2\cos3A\cos2A$

b)

$-2\sin3A\sin2A$

c)

$-2\sin3A\cos2A$

d)

$2\sin2A\cos3A$

5.

If $\cos A=\frac{1}{3}$ , when $\frac{\pi}{2}<A<0$ find $\tan\ \frac{A}{2}$ using the Half-Angle Identity.

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$\frac{\sqrt{2}}{2}$

6.

If $\cos\theta=-\frac{7}{8},$ find the positive value of $\sin\ \frac{\theta}{2}$ using the Half-Angle Identity.

a)

$\frac{4}{15}$

b)

$\frac{\sqrt{15}}{4}$

c)

$\frac{4}{\sqrt{15}}$

d)

$\frac{15}{16}$

7.

Rewrite the angle $\frac{5\pi}{8}$ as if you were going to use the Half-Angle Identities.

a)

$\frac{5\pi}{4}$

b)

$\frac{\frac{5\pi}{4}}{2}$

c)

$\frac{10\pi}{8}$

d)

$\frac{5\pi}{16}$

8.

Use the Sum to Product Identities to rewrite the following: $\cos7\theta+\cos13\theta$

a)

$-2\sin3\theta\cos10\theta$

b)

$-2\cos3\theta\cos10\theta$

c)

$-2\cos3\theta\sin10\theta$

d)

$2\cos10\theta\cos3\theta$

9.

Use a Half-Angle identity to find the exact value of $\tan\ \frac{\theta}{2}$ , given that $\sin\theta=-\frac{3}{5}$ and $\frac{3\pi}{2}<\theta<2\pi$ .

a)

$-\frac{1}{3}$

b)

$-\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$-1$

10.

Use the Half-Angle Identity to find the exact value of $\cos\left(\frac{5\pi}{12}\right)$

a)

$\frac{\sqrt{\sqrt{3}-2}}{2}$

b)

$\frac{\sqrt{2-\sqrt{3}}}{2}$

c)

$-\frac{\sqrt{\sqrt{3}-2}}{2}$

d)

$-\frac{\sqrt{2-\sqrt{3}}}{2}$

Review: Half Angle, Sum to Product & Product to Sum

Total questions: 10

Worksheet time: 20mins

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