Question 1

Which of the following is the standard form of the equation $$x^2 - 8x$$ + $$y^2 + 6y = 11$?

Accepted Answer

$$ (x-4)^2$ + (y+3)^2$ = 38 $$

Question 2

The equation $$x^2 - 8x$$ - $$y^2 + 6y = -8$ represents which type of conic section?

Accepted Answer

Hyperbola

Question 3

What are the coordinates of the foci for the hyperbola $$x^2 - 8x$$ - $$y^2 + 6y = -8$?

Accepted Answer

$$ (4 \pm \sqrt{13}, -3) $$

Question 4

Rewrite $$x^2 - 2x$$ + $$9y^2 + 54y + 46 = 0$ in standard form. Which of the following is correct?

Accepted Answer

$$ \frac{(x-1)^2$}{25} + \frac{(y+3)^2$}{1} = 1 $$

Question 5

Which of the following is the standard form of $$4x - y^2$ + 4y + 16 = 0$$?

Accepted Answer

$$ (y+2)^2$ = 4(x-1) $$

Question 6

For the parabola $$4x - y^2$ + 4y + 16 = 0$$, what are the coordinates of the focus and the equation of the directrix?

Accepted Answer

Focus: $$ (2, -2) $$, Directrix: $$ x = 0 $$

Question 7

Given the parametric equations $$x = -t$$, $$y = t^2$, what is the rectangular equation?

Accepted Answer

$$ y = x^2$ $$

Question 8

Find two angles, one positive and one negative, coterminal with $$	heta = -400^\circ.$$

Accepted Answer

$$ 320^\circ, -40^\circ $$

Question 9

Find two angles, one positive and one negative, coterminal with $$s = 3\pi.$$

Accepted Answer

$$ \pi, -\pi $$

Question 10

Convert $$	heta = 120^\circ to $$radians.

Accepted Answer

$$ \frac{2\pi}{3} $$

Question 11

Convert $$s = -\frac{\pi}{10}$$ radians to degrees.

Accepted Answer

$$ -18^\circ $$

Question 12

Find the complement and supplement of $$	heta = 51^\circ.$$

Accepted Answer

Complement: $$39^\circ$$, Supplement: $$129^\circ$$

Question 13

Find the complement and supplement of $$s = \frac{\pi}{5}.$$

Accepted Answer

Complement: $$\frac{3\pi}{10}$$, Supplement: $$\frac{4\pi}{5}$$

Question 14

Subtract $$13.123^\circ - 6^\circ 51' 39''$$ and express your answer in degrees, minutes, and seconds.

Accepted Answer

$$6^\circ 16' 41''$$

Question 15

Given the terminal point $$\left( \frac{12}{13}, -\frac{5}{13} \right)$$, what is $$\sin s$$?

Accepted Answer

$$ -\frac{5}{13} $$

Question 16

Given the terminal point $$\left( \frac{12}{13}, -\frac{5}{13} ight)$$, what is $$	an s$$?

Accepted Answer

$$ -\frac{5}{12} $$

Question 17

For $$y = 5 \cos \left( 2x - \frac{\pi}{2} \right) - 3$$, what is the amplitude?

Accepted Answer

$$5$$

Question 18

For $$y = 5 \cos \left( 2x - \frac{\pi}{2} \right) - 3$$, what is the period?

Accepted Answer

$$ \pi $$

Question 19

For $$y = -2 \sin(x + \pi) + 1$$, what is the vertical shift?

Accepted Answer

$$1$$

Question 20

For $$y = -2 \sin(x + \pi) + 1$$, what is the amplitude?

Accepted Answer

$$2$$

Precalculus Trigonometry Test 1: Step-by-Step Study Guidance

Study Guide - Practice Questions