Q: Which of the following is the correct double-angle formula for sine?

$$\sin(2\theta) = 2\sin\theta\cos\theta$$

Q: Which of the following is NOT a valid form of the double-angle formula for cosine?

$$\cos(2\theta) = 2\sin^2$\theta + 1$$

Q: Which formula can be used to reduce the power of $$\sin^2$\theta$$?

$$\sin^2$\theta = \frac{1 - \cos(2\theta)}{2}$$

Q: What is the equivalent expression for $$\cos^2$\theta$$ using a power-reducing formula?

$$\cos^2$\theta = \frac{1 + \cos(2\theta)}{2}$$

Q: Which formula is used to find $$\tan\left(\frac{\theta}{2}\right)$$?

$$\tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos\theta}{\sin\theta}$$

Q: Which of the following is the correct half-angle formula for cosine?

$$\cos\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 + \cos\theta}{2}}$$

Q: Which formula can be used to reduce the power of $$\tan^2$\theta$$?

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

Q: Which of the following is the correct double-angle formula for tangent?

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

Question 1

Which of the following is the correct double-angle formula for sine?

Accepted Answer

$$\sin(2	heta) = 2\sin	heta\cos	heta$$

Question 2

Given $$\cos	heta = \frac{3}{5}$$ and $$	heta is in $$quadrant IV, what is $$\sin(2	heta)$$?

Accepted Answer

$$-\frac{24}{25}$$

Question 3

Which of the following is NOT a valid form of the double-angle formula for cosine?

Accepted Answer

$$\cos(2	heta) = 2\sin^2$	heta + 1$$

Question 4

If $$\sin	heta = \frac{4}{5}$$ and $$	heta is in $$quadrant II, what is $$\cos(2	heta)$$?

Accepted Answer

$$-\frac{7}{25}$$

Question 5

Which formula can be used to reduce the power of $$\sin^2$	heta$$?

Accepted Answer

$$\sin^2$	heta = \frac{1 - \cos(2	heta)}{2}$$

Question 6

What is the equivalent expression for $$\cos^2$	heta$$ using a power-reducing formula?

Accepted Answer

$$\cos^2$	heta = \frac{1 + \cos(2	heta)}{2}$$

Question 7

If $$	heta is an $$angle in quadrant III, what is the sign of $$\sin\left(\frac{	heta}{2}ight)$$?

Accepted Answer

Negative

Question 8

Which formula is used to find $$	an\left(\frac{	heta}{2}ight)$$?

Accepted Answer

$$	an\left(\frac{	heta}{2}ight) = \frac{1 - \cos	heta}{\sin	heta}$$

Question 9

A medical device rotates through an angle $$	heta$$ such that $$\sin	heta = 0.6. $$What is $$\sin(2	heta)$$?

Accepted Answer

$$0.8$$

Question 10

If $$\cos	heta = -0.8$$ and $$	heta is in $$quadrant III, what is $$\cos(2	heta)$$?

Accepted Answer

$$0.28$$

Question 11

Which of the following is the correct half-angle formula for cosine?

Accepted Answer

$$\cos\left(\frac{	heta}{2}ight) = \pm \sqrt{\frac{1 + \cos	heta}{2}}$$

Question 12

A chemical reaction produces a wave with $$\sin	heta = 0.5. $$What is $$\cos(2	heta)$$?

Accepted Answer

$$0$$

Question 13

If $$\sin	heta = -0.6$$ and $$	heta is in $$quadrant IV, what is $$\sin(2	heta)$$?

Accepted Answer

$$-0.8$$

Question 14

Which formula can be used to reduce the power of $$	an^2$	heta$$?

Accepted Answer

$$	an^2$	heta = \frac{1 - \cos(2	heta)}{1 + \cos(2	heta)}$$

Question 15

If $$\cos	heta = 0.6$$ and $$	heta is in $$quadrant I, what is $$\cos^2$	heta$$ using a power-reducing formula?

Accepted Answer

$$0.5$$

Question 16

A satellite moves through an angle $$	heta$$ such that $$\cos	heta = 0.3. $$What is $$\sin^2$	heta$$ using a power-reducing formula?

Accepted Answer

$$0.455$$

Question 17

Which of the following is the correct double-angle formula for tangent?

Accepted Answer

$$	an(2	heta) = \frac{2	an	heta}{1 - 	an^2$	heta}$$

Question 18

If $$	heta is in $$quadrant II, what is the sign of $$\cos\left(\frac{	heta}{2}ight)$$?

Accepted Answer

Positive

Analytic Trigonometry: Double-Angle, Power-Reducing, and Half-Angle Formulas

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