Q: A plane photographs a building when the sun's angle of elevation is $$43^\circ$$ and the shadow is $$65$$ feet long. What is the height of the building? (Round to the nearest whole number.)

$$65 \times \tan 43^\circ \approx 60$$ feet

Q: Solve $$8\sin \theta + 1 = 6\sin \theta$$ for $$\theta in$$ $$[0^\circ, 360^\circ). $$What is the solution?

$$\theta = 0^\circ, 270^\circ$$

Question 1

Given the equation $$x^2 - 16x$$ + $$y^2 + 32 = 4$, what type of conic section does this equation represent after completing the square and writing in standard form?

Accepted Answer

A hyperbola

Question 2

Given the equation $$x^2$$ + $$4y^2 - 4y = 8$, what is the center of the conic section after writing it in standard form?

Accepted Answer

$$(0, 0.5)$$

Question 3

A plane photographs a building when the sun's angle of elevation is $$43^\circ$$ and the shadow is $$65$$ feet long. What is the height of the building? (Round to the nearest whole number.)

Accepted Answer

$$65 	imes 	an 43^\circ \approx 60$$ feet

Question 4

Solve for $$	heta in$$ $$0^\circ \u003c 	heta \u003c 360^\circ if$$ $$\cot 	heta = -5.2198. $$Which quadrants contain the solutions?

Accepted Answer

Quadrants II and IV

Question 5

Given $$\sin 	heta = -\frac{7}{5}$$ and $$	heta is in $$quadrant III, what is $$\cos(2	heta)$$?

Accepted Answer

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

Question 6

Solve $$6\cos^2$ x + 7\cos x - 2 = 0$$ for $$x in$$ $$[0^\circ, 360^\circ) by $$factoring. Which is a solution?

Accepted Answer

$$x = 60^\circ$$

Question 7

Solve $$8\sin 	heta + 1 = 6\sin 	heta$$ for $$	heta in$$ $$[0^\circ, 360^\circ). $$What is the solution?

Accepted Answer

$$	heta = 0^\circ, 270^\circ$$

Question 8

Solve $$\sin 2x = -2$$ for $$x in$$ $$[0, 2\pi). $$What is the correct answer?

Accepted Answer

No solution

Question 9

Find the magnitude and direction angle (rounded to the nearest tenth) of the vector $$\langle -2, -6 \rangle.$$

Accepted Answer

Magnitude: $$2\sqrt{10}$$, Direction: $$251.6^\circ$$

Question 10

Compute $$(2\cos 240^\circ + i\sin 240^\circ)(6\cos 140^\circ + i\sin 140^\circ)$$ and give the answer in $$a + bi$$ form rounded to hundredths.

Accepted Answer

$$-8.19 + 2.57i$$

Question 11

Given the point $$(-3, 5)$$, what is $$\sin 	heta$$ for the angle in standard position passing through this point?

Accepted Answer

$$\frac{5}{\sqrt{34}}$$

Question 12

A right triangle has $$A = 29^\circ 13'$$ and $$b = 14.7 yd. $$What is the length of the side opposite angle $$A ($$rounded to the nearest tenth)?

Accepted Answer

$$7.2 yd$$

Question 13

Convert the rectangular point $$(-4, 8) to $$polar coordinates $$(r, 	heta)$$, with $$r as a $$simplified radical and $$	heta$$ rounded to hundredths.

Accepted Answer

$$(4\sqrt{5}, 116.57^\circ)$$

Question 14

Convert the polar point $$(5, 120^\circ) to $$rectangular coordinates $$(x, y). $$Give exact values.

Accepted Answer

$$\left(-\frac{5}{2}, \frac{5\sqrt{3}}{2}\right)$$

Question 15

Given $$\sin 	heta = -\frac{7}{5}$$ and $$	heta is in $$quadrant III, what is $$\cos 	heta$$?

Accepted Answer

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

Question 16

If the major axis of the ellipse $$x^2 + 4(y$$ - $$0.5)^2 = 8$ is vertical, what are the coordinates of the vertices along the major axis?

Accepted Answer

$$(0, 0.5 \pm \sqrt{2})$$

Precalculus Final Exam Review – Step-by-Step Guidance

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