Precalculus Jeopardy 2023 Fall

Trigonometry Function Definitions

100

Given that (x, y) is a point on a circle centered at the origin with radius r, what is y/r?

The ratio of variables equal to Sine.

200

Given that (x, y) is a point on a circle centered at the origin with radius r, what is r/x?

The ratio of variables equal to Secant.

300

Given that (x, y) is a point on a circle centered at the origin with radius r, what is x/y?

The ratio of variables equal to Cotangent.

400

What is sin²x+cos²x?

1

500

Given that (x, y) is a point on a circle centered at the origin with radius r, what is r/y?

The ratio of variables equal to Cosecant.

Quadratic and Polynomials

100

What are the solutions to the equation 4x²=64?

x=4, x=-4

200

What the two factors of the quadratic expression: 

8x²-10x-3

(2x-3) and (4x+1)

300

Find the solutions for the equation: 

5x²+2x+12=0

x=-1/5-i√59/5

x=-1/5+i√59/5

400

State the degree, number of complex roots, and number of real roots of the polynomial given by f(x) = (x-1)(x²+2)(x²-16)

Degree: 5;

Real roots: x = 1, x = 4, x = -4;

Complex roots: x = sqrt(2)i, x = -sqrt(2)i

500

Draw a polynomial graph that could match the polynomial function: f(x) = (x-4)(x+2)(x²+1)

Peer audit 

Radians and Trig Facts

100

What is radian measure of 180 degrees?

pi

200

What is radian measure of 90 degrees?

 pi/2

300

What is degree measure of  3pi/4? 

135 degrees.

400

What is radian measure of 330 degrees?

 11*pi/6

500

What are the two ancient civilizations that discovered trigonometry? 

Babylon and Egypt

Function

100

What is an equation for the squaring function shifted up by 2 units?

f(x)=x²+2

200

What is an equation for the absolute value function shifted to the left by 20 units? 

f(x)=|x+20|

300

If f(x)=x² and g(x)=x-2, what is the equation for f(g(x))?

f(g(x))=(x-2)²

400

Given an example of fifth degree polynomial with three terms.

Answers may vary (peer audit)

500

Give a polynomial equation whose zeros would be 5, -4, 3i. Write your answer in general form (expanded), and suppose leading coefficient a=1. 

y=x⁴-x³-11x²-9x-180

Unit Circle

100

On a unit circle, what is the x coordinate for 30 degrees?

√3/2

200

On a unit circle, what is x coordinate for 60 degrees?

1/2

300

On a unit circle, what is y coordinate for 1620 degrees?

0

400

If sec x=-2 and cot x <0, which quadrant is the angle x terminating in? 

Quadrant II

500

What is the origins of the word Trigonometry?

Greek words:

Trigonon (triangle)

Metron (measure)