Q: Given $$\tan \theta = \frac{7}{6}$$ and $$\theta is a $$third quadrant angle, which of the following is the correct value for $$\sin \theta$$?

$$\sin \theta = -\frac{7}{\sqrt{85}}$$

Q: A 100.0 mg sample of sodium-24 is isolated at 8AM. At 11AM, 87.06 mg remains. What is the decay constant $$k in $$the formula $$q(t) = q_0$ e$$^{kt}$$?

$$k = -0.045$$ \text{ per hour}$

Q: Given the point $$(-6, 7) on $$the terminal side of angle $$\theta in $$standard position, what is $$\sin \theta$$?

$$\sin \theta = \frac{7}{\sqrt{85}}$$

Q: Given two sides of a right triangle are $$a = 5$$ and $$b = 12$$, what is $$\cos \theta$$ where $$\theta is $$the angle opposite side $$a$$?

$$\cos \theta = \frac{12}{13}$$

Q: Given $$\tan \theta = \frac{7}{6}$$ and $$\theta is in $$the third quadrant, what is $$\cos \theta$$?

$$\cos \theta = -\frac{6}{\sqrt{85}}$$

Question 1

Given $$	an 	heta = \frac{7}{6}$$ and $$	heta is a $$third quadrant angle, which of the following is the correct value for $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -\frac{7}{\sqrt{85}}$$

Question 2

If $$\cot$$^{-1}$$(-1.47) is $$evaluated, which quadrant does the resulting angle lie in?

Accepted Answer

Second quadrant

Question 3

Given the function $$y = -2 \cos(2x - \pi)$$, what is the amplitude?

Accepted Answer

$$2$$

Question 4

For the function $$y = -2 \cos(2x - \pi)$$, what is the period?

Accepted Answer

$$\pi$$

Question 5

A cake flan comes out of the oven at $$350^\circ F$$ and is placed in a room at $$70^\circ F. $$After 30 minutes, its temperature is $$240^\circ F. $$Using Newton's Law of Cooling, which equation models the temperature $$T(t) at $$time $$t$$ minutes?

Accepted Answer

$$T(t) = 70 + 280e$$^{-kt}$$

Question 6

Given the cake flan scenario, what is the temperature of the flan 60 minutes after removal from the oven? (Use $$T(t) = 70 + 280e$$^{-kt}$$ and T(30) = 240$ to solve for k$ first.)

Accepted Answer

$$T(60) \approx 166^\circ F$$

Question 7

A 100.0 mg sample of sodium-24 is isolated at 8AM. At 11AM, 87.06 mg remains. What is the decay constant $$k in $$the formula $$q(t) = q_0$ e$$^{kt}$$?

Accepted Answer

$$k = -0.045$$ 	ext{ per hour}$

Question 8

Using the decay formula $$q(t) = 100e$$^{-0.045t}$$, estimate the quantity of sodium-24 remaining at 1PM (5 hours after isolation).

Accepted Answer

$$q(5) \approx 80.2 mg$$

Question 9

What is the half-life of sodium-24 given the decay constant $$k = -0.045$$ per hour?

Accepted Answer

$$t_{1/2} = \frac{\ln 2}{0.045}$$

Question 10

Given the point $$(-6, 7) on $$the terminal side of angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \frac{7}{\sqrt{85}}$$

Question 11

If $$	an 2x = 1$$, what is the general solution for $$x in$$ $$[0, 2\pi)$$?

Accepted Answer

$$x = \frac{\pi}{8}, \frac{5\pi}{8}, \frac{9\pi}{8}, \frac{13\pi}{8}$$

Question 12

What is the phase shift of $$y = -2 \cos(2x - \pi)$$?

Accepted Answer

$$\frac{\pi}{2} to $$the right

Question 13

Given two sides of a right triangle are $$a = 5$$ and $$b = 12$$, what is $$\cos 	heta$$ where $$	heta is $$the angle opposite side $$a$$?

Accepted Answer

$$\cos 	heta = \frac{12}{13}$$

Question 14

Evaluate $$\csc(3.11) to $$two decimal places.

Accepted Answer

$$-1.00$$

Question 15

Which interval represents all possible values of $$x$$ for $$\ln(x) to be $$defined?

Accepted Answer

$$(0, \infty)$$

Question 16

If $$\cos$$^{-1}$$(-.88) is $$calculated, what is the principal value in radians?

Accepted Answer

$$2.64$$

Question 17

Which of the following best describes the graph of $$y = -2 \cos(2x - \pi)$$?

Accepted Answer

A cosine graph with amplitude 2, period $$\pi$$, phase shift $$\frac{\pi}{2}$$ right, reflected over the x-axis

Question 18

If $$\cot$$^{-1}$$(2.03) is $$evaluated, which of the following is closest to the value in radians?

Accepted Answer

$$0.46$$

Question 19

Given $$	an 	heta = \frac{7}{6}$$ and $$	heta is in $$the third quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = -\frac{6}{\sqrt{85}}$$

Precalculus Study Guide: Trigonometry, Graphs, and Exponential Models

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