Q: Solve for all $$\theta in$$ $$[0$$^{\circ}$$, 360$$^{\circ}$$]$$ that satisfy $$2 \cos 2\theta + \sqrt{3} = 0. $$Which of the following is correct?

$$\theta = 15$$^{\circ}$$, 75$$^{\circ}$$, 195$$^{\circ}$$, 255$$^{\circ}$$

Question 1

Solve for all $$x in$$ $$[0, 2\pi]$$ that satisfy the equation $$2 \sin x - \sqrt{3} = 0. $$Which of the following is correct?

Accepted Answer

$$x = \dfrac{\pi}{3}, \dfrac{4\pi}{3}$$

Question 2

Find all solutions for $$x in$$ $$[0, 2\pi] to $$the equation $$\sec x + \sqrt{2} = 0. $$Which values of $$x$$ are solutions?

Accepted Answer

$$x = \dfrac{3\pi}{4}, \dfrac{5\pi}{4}$$

Question 3

A satellite dish is designed so that the angle of elevation to the sun at noon is $$x$$ radians, where $$\sqrt{3} \cot x - 1 = 0. $$For which $$x in$$ $$[0, 2\pi]$$ does this occur?

Accepted Answer

$$x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 4

Solve for all $$x in$$ $$[0, 2\pi]$$ that satisfy $$\sqrt{3} \sin x + \sqrt{3} = 0. $$What are the solutions?

Accepted Answer

$$x = \dfrac{3\pi}{2}$$

Question 5

Find all solutions for $$x in$$ $$[0, 2\pi] to$$ $$\sqrt{2} \csc x - 1 = 0. $$Which of the following is correct?

Accepted Answer

$$x = \dfrac{\pi}{4}, \dfrac{3\pi}{4}$$

Question 6

Solve for all $$	heta in$$ $$[0$$^{\circ}$$, 360$$^{\circ}$$]$$ that satisfy $$2 \cos 2	heta + \sqrt{3} = 0. $$Which of the following is correct?

Accepted Answer

$$	heta = 15$$^{\circ}$$, 75$$^{\circ}$$, 195$$^{\circ}$$, 255$$^{\circ}$$

Question 7

A ramp is built at an angle $$x$$ such that $$5 	an x - 5\sqrt{3} = 0. $$For $$x in$$ $$[0, 2\pi]$$, what are the possible values of $$x$$?

Accepted Answer

$$x = \dfrac{\pi}{3}, \dfrac{4\pi}{3}$$

Question 8

Solve for all $$x in$$ $$[0, 2\pi]$$ that satisfy $$2 \cos 2x - 1 = 0. $$Which of the following is correct?

Accepted Answer

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

Question 9

Solve the inequality $$1 - 2\sin x \u003e 0$$ for $$x in$$ $$[0, 2\pi]. $$Which interval describes all solutions?

Accepted Answer

$$x \in [0, \dfrac{\pi}{6}) \cup (\dfrac{11\pi}{6}, 2\pi)$$

Question 10

Solve the inequality $$\sqrt{3} \cot x - 1 \leq 0$$ for $$x in$$ $$[0, 2\pi]. $$Which interval describes all solutions?

Accepted Answer

$$x \in [\dfrac{\pi}{6}, \dfrac{5\pi}{6}] \cup [\dfrac{7\pi}{6}, \dfrac{11\pi}{6}]$$

Question 11

Evaluate $$\arccos\left(-\dfrac{\sqrt{2}}{2}\right). $$What is the answer in radians?

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 12

Evaluate $$	an(	an$$^{-1}$$ 5). $$What is the result?

Accepted Answer

$$5$$

Question 13

Evaluate $$	an$$^{-1}$$\left(	an\dfrac{3\pi}{5}ight). $$What is the answer in radians?

Accepted Answer

$$\dfrac{3\pi}{5} - \pi = -\dfrac{2\pi}{5}$$

Question 14

Evaluate $$\sec(\arccot 2). $$What is the value?

Accepted Answer

$$\sqrt{5}$$

Question 15

Evaluate $$\arctan(-1). $$What is the answer in radians?

Accepted Answer

$$-\dfrac{\pi}{4}$$

Question 16

Evaluate $$\sin(\sin$$^{-1}$$ 0.3). $$What is the result?

Accepted Answer

$$0.3$$

Question 17

Evaluate $$\cos$$^{-1}$$\left(\cos\dfrac{7\pi}{5}\right). $$What is the answer in radians?

Accepted Answer

$$\dfrac{3\pi}{5}$$

Question 18

Evaluate $$\sin(\arcsec 7). $$What is the value?

Accepted Answer

$$\dfrac{\sqrt{48}}{7}$$

Question 19

Given triangle $$ABC$$ with $$a = 1.23$$, $$A = 67$$^{\circ}$$, B$$ = $$76^{\circ}$$, solve for $$b (to $$two decimal places).

Accepted Answer

$$b = 1.36$$

Question 20

Given triangle $$ABC$$ with $$a = 8$$, $$c = 6$$, $$B = 45$$^{\circ}$$, solve for b$ (to the nearest tenth).

Accepted Answer

$$b = 7.2$$

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