Free Printable Quiz 4 Grade 12

1.

Rewrite $\cos4\theta\ \sin6\theta$ using the product-to-sum formula.

a)

$\frac{1}{2}\left[\sin2\theta\ +\cos10\theta\right]$

b)

$\frac{1}{2}\left[\cos10\theta-\cos\left(-2\theta\right)\right]$

c)

$\frac{1}{2}\left[\sin10\theta-\sin\left(-2\theta\right)\right]$

d)

$\frac{1}{2}\left[\sin4\theta-\cos6\theta\right]$

2.

Rewrite sin 9x + sin 3x using a sum-to-product formula.

a)

2 cos 6x sin 3x

b)

2 cos 9x cos 3x

c)

2 sin 12x cos 6x

d)

2 sin 6x cos 3x

3.

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)

$2\cos10\theta\cos3\theta$

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.

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)

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

6.

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)

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

7.

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)

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

8.

Write the following product as a sum:

$\cos75+\cos15$

a)

$2\sin45\cos30$

b)

$2\cos45\sin30$

c)

$2\cos45\cos30$

d)

$-2\sin45\sin30$

9.

Write the following product as a sum:

$\sin60-\sin45$

a)

$2\sin\frac{105}{2}\cos\frac{15}{2}$

b)

$2\cos\frac{105}{2}\sin\frac{15}{2}$

c)

$2\cos\frac{105}{2}\cos\frac{15}{2}$

d)

$-2\sin\frac{105}{2}\sin\frac{15}{2}$

10.

(cos 2x -cos 4x)/(sin 2x + sin 4x)

a)

tan x

b)

- tan x

c)

cot x

d)

cot x

Quiz 4 Grade 12

Total questions: 10

Worksheet time: 48mins

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