Trigonometry Quiz
Questions: 16 · 10 minutes
1. What is the period of y = sin(2x), with x measured in radians?
Two complete π-radian intervals
Half of a π-radian interval
One π-radian interval
Four complete π-radian intervals
2. What is the amplitude of y = −3cos(x) + 1?
2 units
1 unit
4 units
3 units
3. What is the exact value of sin(30°)?
1/2
√3/2
√2/2
1
4. Which values solve 2sin(x) = 1 for 0° ≤ x < 360°?
30° and 150°
150° only
60° and 120°
30° only
5. Two sides of a triangle have lengths 5 and 7, and their included angle is 60°. According to the Law of Cosines, what is the length of the opposite side?
√39
√74
√109
6
6. A right triangle has a side of length 6 opposite θ and a hypotenuse of length 10. What is sin(θ)?
3/5
4/5
3/4
5/3
7. What is 150° expressed in radians?
3π/4
4π/5
6π/5
5π/6
8. Which statement gives a Pythagorean trigonometric identity?
The sine and cosine values always add to 1
The squares of the sine and cosine values add to 1
The square of the tangent value plus 1 equals the tangent value
The squares of the sine and cosine values differ by 1
9. From a point on level ground 20 meters from the base of a tower, the angle of elevation to the top is 35°. Ignoring eye height, which expression gives the tower's height h?
h = 20sin(35°)
h = 20cos(35°)
h = 20/tan(35°)
h = 20tan(35°)
10. For an acute angle θ, tan(θ) = 3/4. If the adjacent side has length 8, what is the length of the opposite side?
4
32/3
8
6
11. An angle θ lies in Quadrant II and cos(θ) = −3/5. What is sin(θ)?
1/5
3/5
4/5
5/4
12. A 5-meter ladder rests against a wall, with its foot 3 meters from the wall. What is the sine of the angle between the ladder and the ground?
3/5
4/3
4/5
5/4
13. A point on the unit circle corresponds to an angle of 120°. What are the signs of its x- and y-coordinates?
Both coordinates are positive
The x-coordinate is negative and the y-coordinate is positive
The x-coordinate is positive and the y-coordinate is negative
Both coordinates are negative
14. What is the reference angle for 225°?
25°
45°
135°
225°
15. In a triangle, angle A is 30° with opposite side a = 5, while angle B is 45°. Using the Law of Sines, what is the length of side b opposite angle B?
5
5√2
5√3
10
16. In a right triangle, which ratio defines sin(θ)?
Opposite side divided by adjacent side
Adjacent side divided by hypotenuse
Opposite side divided by hypotenuse
Hypotenuse divided by opposite side