Q: A building casts a shadow of 69 ft when the angle of elevation of the sun is $$36^\\circ. $$What is the height of the building?

$$69 \\times \\tan(36^\\circ)$$

Q: A ladder leans against a 10 m wall. The bottom of the ladder is 3.2 m from the wall. What is the angle between the ladder and the wall?

$$\\tan$$^{-1}$$\\left(\\dfrac{3.2}{10}\\right)$$

Q: If $$\\sin(\\theta) = -0.71648873$$, find all values of $$\\theta in$$ $$[0^\\circ, 360^\\circ)$$ that satisfy this equation.

$$180^\\circ + 45.8^\\circ$$ and $$360^\\circ - 45.8^\\circ$$

Q: Which of the following is a Pythagorean identity?

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

Q: Which of the following is a reciprocal identity?

$$\\sin\\theta = \\dfrac{1}{\\csc\\theta}$$

Q: If $$\\cos(\\theta) = 0.5490$$, find all values of $$\\theta in$$ $$[0^\\circ, 360^\\circ).$$

$$56.7^\\circ$$ and $$303.3^\\circ$$

Q: If $$\\cot(\\theta) = 0.4327$$, find all values of $$\\theta in$$ $$[0^\\circ, 360^\\circ).$$

$$66.6^\\circ$$ and $$246.6^\\circ$$

Question 1

A building casts a shadow of 69 ft when the angle of elevation of the sun is $$36^\circ. $$What is the height of the building?

Accepted Answer

$$69 \times \tan(36^\circ)$$

Question 2

Given the point $$(-12, -5) is on $$the terminal side of angle $$\theta in $$standard position, what is $$\sin(\theta)$$?

Accepted Answer

$$\dfrac{-5}{13}$$

Question 3

If $$\tan(\theta) = \dfrac{3}{4}$$ and $$\theta is in $$quadrant III, what is $$\csc(\theta)$$?

Accepted Answer

$$-\dfrac{5}{3}$$

Question 4

Find all exact values of $$\theta in$$ $$[0^\circ, 360^\circ)$$ such that $$\cos(\theta) = \dfrac{\sqrt{3}}{2}.$$

Accepted Answer

$$30^\circ, 330^\circ$$

Question 5

A ladder leans against a 10 m wall. The bottom of the ladder is 3.2 m from the wall. What is the angle between the ladder and the wall?

Accepted Answer

$$\tan$$^{-1}$$\left(\dfrac{3.2}{10}\right)$$

Question 6

Which quadrant must $$\theta$$ lie in if both $$\sin(\theta)$$ and $$\cos(\theta)$$ are negative?

Accepted Answer

Quadrant III

Question 7

If $$\sin(\theta) = -0.71648873$$, find all values of $$\theta in$$ $$[0^\circ, 360^\circ)$$ that satisfy this equation.

Accepted Answer

$$180^\circ + 45.8^\circ$$ and $$360^\circ - 45.8^\circ$$

Question 8

Given $$\tan(19^\circ 45')$$, what is its value rounded to four decimal places?

Accepted Answer

$$0.3590$$

Question 9

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 10

Find the exact value of $$\sin\left(\dfrac{\pi}{2}\right).$$

Accepted Answer

$$1$$

Question 11

If $$\tan(\theta) = -\dfrac{2\sqrt{10}}{5}$$ and $$\sin(\theta) \u003c 0$$, what is the value of $$y$$?

Accepted Answer

$$-2\sqrt{10}$$

Question 12

A ship leaves port and sails on a bearing of $$N40^\circ E at 18 $$knots for 1.5 hours. Another ship leaves at the same time and sails on a bearing of $$S50^\circ E at 26 $$knots for 1.5 hours. How far apart are they after 1.5 hours?

Accepted Answer

$$47$$ nautical miles

Question 13

Find the exact value of $$\sec\left(\dfrac{2\pi}{3}\right).$$

Accepted Answer

$$-2$$

Question 14

Which of the following is a reciprocal identity?

Accepted Answer

$$\sin\theta = \dfrac{1}{\csc\theta}$$

Question 15

If $$\cos(\theta) = 0.5490$$, find all values of $$\theta in$$ $$[0^\circ, 360^\circ).$$

Accepted Answer

$$56.7^\circ$$ and $$303.3^\circ$$

Question 16

Find the amplitude of the function $$y = 3 + 5\sin\left(\pi x + \dfrac{\pi}{4}\right).$$

Accepted Answer

$$5$$

Question 17

Find the period of the function $$y = 2\tan\left(x + \dfrac{\pi}{4}\right).$$

Accepted Answer

$$\pi$$

Question 18

If $$\cot(\theta) = 0.4327$$, find all values of $$\theta in$$ $$[0^\circ, 360^\circ).$$

Accepted Answer

$$66.6^\circ$$ and $$246.6^\circ$$

Question 19

A plane flies 1.7 hours at 120 mph on a bearing of $$40^\circ$$, then turns and flies 2.0 hours at the same speed on a bearing of $$130^\circ. $$How far is the plane from its starting point?

Accepted Answer

$$315$$ miles

Precalculus Trigonometry: Angles, Triangles, and Trigonometric Functions

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