Trigonometric Functions Quiz

Grade 11 · Math · Quiz

10 questions covering trig ratios, radian conversion, the unit circle, and key identities.

Questions

What is tan(45 degrees)?
1. sqrt(2)/2
2. sqrt(3)
3. 1
4. 0
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Answer: 1
tan(45) = sin(45)/cos(45) = (sqrt(2)/2)/(sqrt(2)/2) = 1.
Convert 3*pi/4 radians to degrees.
1. 120
2. 135
3. 150
4. 270
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Answer: 135
(3*pi/4) * (180/pi) = 3*180/4 = 135 degrees.
On the unit circle, what is sin(pi)?
1. 1
2. -1
3. 0
4. pi
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Answer: 0
At theta = pi, the point is (-1, 0). y-coordinate = sin(pi) = 0.
What is the amplitude of y = 4*sin(x)?
1. 1
2. 2
3. 4
4. pi
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Answer: 4
Amplitude = |A| in y = A*sin(x). Here A = 4, amplitude = 4.
Simplify using a Pythagorean identity: 1 - cos^2(theta).
1. sin^2(theta)
2. tan^2(theta)
3. sec^2(theta)
4. cos(theta)
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Answer: sin^2(theta)
From sin^2 + cos^2 = 1: 1 - cos^2 = sin^2.
In which quadrant is sin(theta) < 0 and cos(theta) > 0?
1. Quadrant I
2. Quadrant II
3. Quadrant III
4. Quadrant IV
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Answer: Quadrant IV
Quadrant IV: x > 0 (cos > 0) and y < 0 (sin < 0).
What is cos(0)?
1. 0
2. 1
3. -1
4. undefined
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Answer: 1
At theta = 0, the unit circle point is (1, 0). cos(0) = 1.
The period of y = tan(x) is:
1. 2*pi
2. pi
3. pi/2
4. 4*pi
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Answer: pi
The tangent function repeats every pi radians.
Which identity equals 1 + tan^2(theta)?
1. sin^2(theta)
2. sec^2(theta)
3. csc^2(theta)
4. cos^2(theta)
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Answer: sec^2(theta)
Divide sin^2 + cos^2 = 1 by cos^2: tan^2 + 1 = sec^2.
What is sin(7*pi/6)?
1. 1/2
2. sqrt(3)/2
3. -1/2
4. -sqrt(3)/2
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Answer: -1/2
7*pi/6 = pi + pi/6 (Quadrant III). sin(pi + pi/6) = -sin(pi/6) = -1/2.

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