Q: If $$\sin(\theta) = \dfrac{3}{5}$$ and $$\theta is in $$Quadrant II, what is $$\cos(\theta)$$?

$$\cos(\theta) = -\dfrac{4}{5}$$

Q: Which of the following is the correct expression for the double angle identity for sine?

$$\sin(2\theta) = 2\sin(\theta)\cos(\theta)$$

Question 1

Which of the following best describes the primary focus of Precalculus as taught in MAC 1147 at Hillsborough College?

Accepted Answer

Preparation for calculus through the study of functions, trigonometry, and analytical geometry.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is the value of $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 3

Which of the following equations represents the unit circle in the $$xy-$$plane?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 4

A Ferris wheel has a radius of 20 meters and rotates once every 2 minutes. If a rider starts at the lowest point, which trigonometric function best models the rider's height above the ground as a function of time $$t (in $$minutes)?

Accepted Answer

$$h(t) = 20 \cos(\pi t) + 20$$

Question 5

Which of the following is the correct formula for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ $$(r 
eq 1)$$ for $$n$$ terms?

Accepted Answer

$$S_n = \dfrac{a(1 - r^n)}{1 - r}$$

Question 6

If $$\sin(	heta) = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$\cos(	heta) = -\dfrac{4}{5}$$

Question 7

Which of the following is the correct inverse function of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 7}{3}$$

Question 8

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 9

Which of the following is the correct solution to the equation $$2\cos^2$(x) - 1 = 0$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = 0, \pi$$

Question 10

A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?

Accepted Answer

$$25$$

Question 11

Which of the following is the correct expression for the double angle identity for sine?

Accepted Answer

$$\sin(2	heta) = 2\sin(	heta)\cos(	heta)$$

Question 12

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 13

Which of the following is the correct formula for the distance between the points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 14

A ball is thrown upward with an initial velocity of 32 ft/s from a height of 48 ft. The height $$h$$ after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t + 48. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 1$$

Question 15

Which of the following is the correct formula for the area of a triangle given two sides $$a$$ and $$b$$ and the included angle $$C$$?

Accepted Answer

$$A = \dfrac{1}{2}ab\sin(C)$$

Precalculus & Trigonometry Course Schedule and Structure

Guida di studio - Domande di pratica

Study guide - Flashcard