Question 1

Solve the equation $$4 \sin^2$ x - 3 = 0$$ for $$x in$$ $$[0, 2\pi). $$Which set of solutions is correct?

Accepted Answer

$$x = \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}$$

Question 2

Solve the equation $$\sqrt{2} \cos x \sin x + \cos x = 0$$ for $$x in$$ $$[0, 2\pi). $$Which set of solutions is correct?

Accepted Answer

$$x = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{4}, \frac{7\pi}{4}$$

Question 3

Solve the equation $$\cos 3x = \frac{1}{2}$$ for $$x in$$ $$[0^\circ, 360^\circ). $$Which set of solutions is correct?

Accepted Answer

$$x = 20^\circ, 100^\circ, 140^\circ, 220^\circ, 260^\circ, 340^\circ$$

Question 4

Given $$\frac{\sin 63^\circ}{a} = \frac{\sin 52^\circ}{7}$$, solve for $$a.$$

Accepted Answer

$$a = 7.92$$

Question 5

Find the area of a triangle if $$A = 21.3^\circ$$, $$c = 4.3 in$$, and $$b = 6.3 in.$$

Accepted Answer

$$9.8\ 	ext{in}^2$$

Question 6

How many triangles are possible if $$a = 20$$, $$b = 12$$, and $$B = 25^\circ$$?

Accepted Answer

1

Question 7

How many triangles are possible if $$c = 35$$, $$a = 21$$, and $$A = 62^\circ$$?

Accepted Answer

1

Question 8

How many triangles are possible if $$b = 10$$, $$c = 13$$, and $$C = 42^\circ$$?

Accepted Answer

1

Question 9

Find the missing parts of the triangle if $$A = 42^\circ$$, $$a = 6$$, and $$b = 3. ($$Round answers to nearest whole number)

Accepted Answer

$$B = 21^\circ, C = 117^\circ, c = 7$$

Question 10

Find angle $$B if$$ $$a = 3.1$$, $$b = 7.3$$, and $$c = 5.4.$$

Accepted Answer

$$65.5^\circ$$

Question 11

Find the area of the triangle if $$a = 8 in$$, $$b = 12 in$$, and $$c = 16 in.$$

Accepted Answer

$$12\sqrt{15}\ 	ext{in}^2$$

Question 12

Find the horizontal and vertical components of the vector if $$	heta = 203^\circ$$ and $$|\mathbf{v}| = 6.$$

Accepted Answer

$$\langle -5.5, -2.3 \rangle$$

Question 13

Find the dot product between the vectors $$\langle 4, -2 \rangle$$ and $$\langle -1, 6 \rangle.$$

Accepted Answer

$$-14$$

Question 14

Find the angle between the vectors $$\langle 4, 2 \rangle$$ and $$\langle -1, 2 \rangle.$$

Accepted Answer

$$90^\circ$$

Question 15

Are the vectors $$\langle -4, 6 \rangle$$ and $$\langle 3, -2 \rangle$$ orthogonal?

Accepted Answer

Yes

Question 16

Use the unit circle to solve: $$\sin x = \frac{1}{2}$$ for $$x in$$ $$[0^\circ, 360^\circ). $$Which values are correct?

Accepted Answer

$$x = 30^\circ, 150^\circ$$

Question 17

Use the unit circle to solve the equation $$2 \cos^2$ x - \cos x = 0$$ for $$x in$$ $$[0^\circ, 360^\circ). $$Which values are correct?

Accepted Answer

$$x = 0^\circ, 60^\circ, 300^\circ$$

Question 18

Find side $$c if$$ $$A = 32^\circ$$, $$B = 59^\circ$$, and $$b = 4.2 cm. $$Round to one decimal place.

Accepted Answer

$$c = 6.7 cm$$

Question 19

Find the magnitude and direction for the vector $$\mathbf{u} = \langle -5, -5 \rangle. $$Round magnitude to a whole number and direction to the nearest degree.

Accepted Answer

Magnitude: $$7$$, Direction: $$225^\circ$$

Trigonometry Test #4 Review – Laws of Sines and Cosines, Vectors, and Trigonometric Equations

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