Trigonometry Jeopardy

A free trigonometry review game on right triangles, the unit circle, radians, and identities. Put it on the projector and students buzz in by phone.

6 categories · 30 clues · Final Jeopardy · everyone buzzes in from their phone

For the classroom

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Every clue on this board

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SOH CAH TOA

$200
In a right triangle, the sine of an angle equals the opposite side divided by this side.
What is the hypotenuse?
$400
This trigonometric ratio equals the opposite side divided by the adjacent side.
What is tangent?
$600
In a 3-4-5 right triangle, the sine of the angle opposite the side of length 3 is this.
What is 3/5?
$800
A 13-foot ladder reaches 12 feet up a wall, and the cosine of the angle it makes with the ground is this fraction.
What is 5/13?
$1,000
This reciprocal of sine equals the hypotenuse divided by the opposite side.
What is cosecant?

Special Right Triangles

$200
In a 45-45-90 triangle with legs of length 1, the hypotenuse has this length.
What is the square root of 2?
$400
In a 30-60-90 triangle, the hypotenuse is this many times as long as the shorter leg.
What is 2?
$600
A 30-60-90 triangle has a shorter leg of 4, so its longer leg has this exact length.
What is 4 times the square root of 3?
$800
A 45-45-90 triangle has a hypotenuse of 10, so each leg has this exact length.
What is 5 times the square root of 2?
$1,000
Read from a 30-60-90 triangle, the exact value of the sine of 60 degrees is this.
What is the square root of 3 over 2?

Degrees and Radians

$200
A full circle measures 360 degrees, or this many radians.
What is 2 pi?
$400
One radian is roughly this many degrees, rounded to the nearest whole number.
What is 57 degrees?
$600
An angle of pi over 6 radians is equal to this many degrees.
What is 30 degrees?
$800
To convert an angle from degrees to radians, multiply by this fraction.
What is pi over 180?
$1,000
An angle of 5 pi over 4 radians is equal to this many degrees.
What is 225 degrees?

The Unit Circle

$200
The unit circle is centered at the origin and has this point at an angle of 90 degrees.
What is (0, 1)?
$400
On the unit circle, the y-coordinate of the point at a given angle equals this function of the angle.
What is sine?
$600
Sine is negative and cosine is positive for angles ending in this quadrant.
What is the fourth quadrant?
$800
Because the x-coordinate at 90 degrees is zero, the tangent of 90 degrees is this.
What is undefined?
$1,000
The point on the unit circle at an angle of 2 pi over 3 has this x-coordinate.
What is negative one-half?

Trig Identities

$200
The identity sine squared x plus cosine squared x equals 1 goes by this name, after a Greek mathematician.
What is the Pythagorean identity?
$400
One plus tangent squared x is equal to this.
What is secant squared x?
$600
Because sine is an odd function, the sine of negative x is equal to this.
What is negative sine x?
$800
The double-angle formula lets you write cosine of 2x as 1 minus 2 times this.
What is sine squared x?
$1,000
The tangent of A plus B equals tan A plus tan B divided by this expression.
What is 1 minus tan A tan B?

Graphs of Sine and Cosine

$200
The horizontal length of one full cycle of a sine graph, 2 pi for y = sin x, is called this.
What is the period?
$400
The graph of y = 3 sin x has this amplitude.
What is 3?
$600
The graph of y = sin 2x completes one full cycle over an interval of this length.
What is pi?
$800
A horizontal shift of a sine or cosine graph is called this.
What is a phase shift?
$1,000
The graph of y = cos x is the graph of y = sin x shifted left by this amount.
What is pi over 2?

Final Jeopardy — Cofunctions

In any right triangle, the sine of one acute angle is equal to this trigonometric function of the other acute angle.

What is cosine?

How to run this board

Six columns cover the core of a trig unit: right-triangle ratios, special right triangles, converting between degrees and radians, reading the unit circle, the basic identities, and the amplitude and period of sine and cosine graphs.

Most clues need a quick calculation, so allow calculators only where the class would use one on the test and say so up front. Give each team a whiteboard and require a correct final answer written down before the team's buzz counts.

For the unit circle column, a house rule that pays off: answers must be exact values, not decimals. It is the habit the next test will reward.

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