Math · Drill 47

Math practice 47

98 questions ~15 min recommended

⏱ 00:00

Score

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1. What is the period of the trigonometric function $f(x) = 3\sin\!\left(\dfrac{\pi}{2}x\right) - 4$?

A. $$\frac{\pi}{2}$

B. $$2$

C. $$4$

D. $$3$

2. The function $g(x) \= -3\cos\!\left(\dfrac{\pi}{2}x\right) + k$ has a minimum value of 1. What is the maximum value of $g(x)$?

A. 4

B. 5

C. 7

D. 10

3. Which equals $\sin(60^\circ)$?

A. $$\frac{1}{2}$

B. $$\sqrt{3}$

C. $$\frac{\sqrt{3}}{2}$

D. $$\frac{\sqrt{2}}{2}$

4. In a right triangle, angle $\theta$ has adjacent side length $12$ and hypotenuse length $13$. What is $\cos(\theta)$?

A. $$\frac{12}{5}$

B. $$\frac{5}{13}$

C. $$\frac{13}{12}$

D. $$\frac{12}{13}$

5. In a right triangle, the side opposite angle $\theta$ is $8$ and the hypotenuse is $17$. What is $\sin(\theta)$?

A. $$\frac{15}{17}$

B. $$\frac{17}{8}$

C. $$\frac{8}{15}$

D. $$\frac{8}{17}$

6. What is $\tan(\frac{\pi}{4})$?

A. $$\sqrt{3}$

B. $$\frac{\sqrt{3}}{2}$

C. $$0$

D. $$1$

7. In the unit circle, what is $\sin(\frac{\pi}{6})$?

A. √3/2

B. √2/2

C. 0

D. 1/2

8. What is $\sin(90^\circ)$?

A. 0

B. 1

C. $$\frac{1}{2}$

D. $$-1$

9. What is $\sin(30^\circ)$?

A. $$\frac{\sqrt{3}}{2}$

B. $$0$

C. $$\frac{1}{2}$

D. $$\frac{\sqrt{2}}{2}$

10. In a right triangle, if the opposite side to angle $\theta$ is 5 and the adjacent side is 12, what is $\tan(\theta)$?

A. 5/13

B. 5/12

C. 12/5

D. 13/5

11. In a right triangle, the hypotenuse is $10$ and the side adjacent to angle $\theta$ is $6$. What is $\sin(\theta)$?

A. $$\frac{3}{5}$

B. $$\frac{5}{3}$

C. $$\frac{4}{5}$

D. $$\frac{6}{10}$

12. Which equals $\sin(90^\circ)$?

A. 1/2

B. 1

C. 0

D. √2/2

13. In the right triangle, if the opposite side is 7 and the adjacent side is 24, what is $\tan(\theta)$?

A. $$\frac{7}{25}$

B. $$\frac{7}{24}$

C. $$\frac{25}{7}$

D. $$\frac{24}{7}$

14. In a right triangle, if the opposite side to angle $\theta$ is 9 and the adjacent side is 12, what is $\tan(\theta)$?

A. 9/12

B. 3/4

C. 4/3

D. 12/9

15. What is $\cos(60^\circ)$?

A. $$\frac{\sqrt{3}}{2}$

B. $$1$

C. $$\frac{\sqrt{2}}{2}$

D. $$\frac{1}{2}$

16. What angle has $\tan(\theta) = 1$?

A. $$45^\circ$

B. $$30^\circ$

C. $$60^\circ$

D. $$90^\circ$

17. What angle $\theta$ (in degrees) has $\sin(\theta)=\frac{\sqrt{2}}{2}$, where $0^\circ \le \theta \le 90^\circ$?

A. $$90^\circ$

B. $$30^\circ$

C. $$45^\circ$

D. $$60^\circ$

18. In a right triangle, if the opposite side to angle $\theta$ is 6 and the hypotenuse is 10, what is $\sin(\theta)$?

A. 3/5

B. 4/5

C. 5/6

D. 6/5

19. A right triangle has legs of lengths $5$ (adjacent to angle $\theta$) and $12$ (opposite to angle $\theta$). What is $\cos(\theta)$?

A. $$\frac{13}{5}$

B. $$\frac{5}{12}$

C. $$\frac{12}{13}$

D. $$\frac{5}{13}$

20. Which equals $\cos\left(\frac{\pi}{3}\right)$?

A. $$1$

B. $$\frac{\sqrt{2}}{2}$

C. $$\frac{1}{2}$

D. $$\frac{\sqrt{3}}{2}$

21. Which equals $\sin(\pi/6)$?

A. 1

B. $$\frac{\sqrt{3}}{2}$

C. $$\frac{1}{2}$

D. $$\frac{\sqrt{2}}{2}$

22. What is $\tan(90^\circ)$?

A. Undefined

B. $$\infty$

C. 1

D. 0

23. What is $\tan\left(\frac{\pi}{4}\right)$?

A. $$0$

B. $$\frac{\sqrt{3}}{3}$

C. $$\sqrt{3}$

D. $$1$

24. In a right triangle, the angle $\theta$ has opposite side length $3$ and adjacent side length $4$. What is $\tan(\theta)$?

A. $$\frac{3}{4}$

B. $$\frac{3}{5}$

C. $$\frac{4}{5}$

D. $$\frac{4}{3}$

25. Which equals $\cos\left(\frac{\pi}{2}\right)$?

A. $$-1$

B. $$1$

C. $$0$

D. $$\frac{\sqrt{2}}{2}$

26. What is $\tan(0^\circ)$?

A. 0

B. √3/2

C. √3

D. 1

27. What angle $\theta$ satisfies $\sin(\theta)=\frac{\sqrt{2}}{2}$, where $\theta$ is a common acute angle?

A. $$45^\circ$

B. $$90^\circ$

C. $$30^\circ$

D. $$60^\circ$

28. In the right triangle, if the opposite side is 6 and the adjacent side is 8, what is $\tan(\theta)$?

A. $$\frac{8}{6}$

B. $$\frac{4}{3}$

C. $$\frac{3}{4}$

D. $$\frac{6}{8}$

29. Which equals $\tan\left(45^\circ\right)$?

A. $$1$

B. $$\sqrt{3}$

C. $$0$

D. $$\frac{\sqrt{3}}{3}$

30. Which equals $\sin(0^\circ)$?

A. $$\frac{1}{2}$

B. $$0$

C. $$\frac{\sqrt{2}}{2}$

D. $$1$

31. In the right triangle, if the adjacent side is 9 and the hypotenuse is 15, what is $\cos(\theta)$?

A. $$0.75$

B. $$0.8$

C. $$0.5$

D. $$0.6$

32. Which of the following expresses $60°$ in radians?

A. $$\frac{\pi}{6}$

B. $$\frac{\pi}{2}$

C. $$\frac{\pi}{4}$

D. $$\frac{\pi}{3}$

33. What is $\sin(0^\circ)$?

A. $$1/2$

B. $$\sqrt{2}/2$

C. $$1$

D. $$0$

34. What is the maximum value of the trigonometric function $y = -3\sin(2x) + 4$?

A. 1

B. 3

C. 4

D. 7

35. In $\triangle ABC$, the length of side $a$ is 5, the length of side $b$ is 7, and the measure of $\angle C$ is $60°$. What is the length of side $c$?

A. $$\sqrt{39}$

B. $$\sqrt{109}$

C. $$8$

D. $$\sqrt{74}$

36. For an angle $\theta$ such that $0 < \theta < \dfrac{\pi}{2}$, it is known that $\sin(\theta) = \dfrac{3}{5}$. What is the value of $\cos(\theta) + \tan(\theta)$?

A. $$\dfrac{7}{5}$

B. $$\dfrac{31}{20}$

C. $$1$

D. $$2$

37. In triangle $ABC$, the right angle is at $B$. The length of $\overline{AB}$ is 8 units and the length of $\overline{BC}$ is 15 units. What is the value of $\tan C$?

A. $$\frac{8}{15}$

B. $$\frac{15}{17}$

C. $$\frac{8}{17}$

D. $$\frac{15}{8}$

38. In $\triangle PQR$, $\angle P \= 30^\circ$, $\angle Q \= 120^\circ$, and $\angle R \= 30^\circ$.  If side $p$ (opposite $\angle P$) has a length of 5, what is the length of side $q$ (opposite $\angle Q$)?

A. $$10$

B. $$5$

C. $$5\sqrt{2}$

D. $$5\sqrt{3}$

39. Which of the following expresses $150°$ in radians?

A. $$\frac{3\pi}{4}$

B. $$\frac{5\pi}{6}$

C. $$\frac{7\pi}{6}$

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

40. For an acute angle $\theta$ in a right triangle, it is given that $\tan \theta = \frac{3}{4}$. What is the value of $\sin \theta$?

A. $$\frac{3}{7}$

B. $$\frac{4}{5}$

C. $$\frac{3}{5}$

D. $$\frac{4}{3}$

41. Which equals $\cos(90^\circ)$?

A. 1/2

B. 1

C. 0

D. √3/2

42. Which equals $\cos(\pi/3)$?

A. $$\frac{\sqrt{2}}{2}$

B. $$\frac{1}{2}$

C. $$\frac{\sqrt{3}}{2}$

D. $$1$

43. What is $\sin(\theta)$ for the right triangle shown, where the opposite side is 3 and the hypotenuse is 5?

A. 0.5

B. 0.6

C. 0.75

D. 0.8

44. In the right triangle, if the opposite side is 8 and the hypotenuse is 17, what is $\sin(\theta)$?

A. $$\frac{15}{17}$

B. $$\frac{8}{17}$

C. $$\frac{8}{15}$

D. $$\frac{17}{8}$

45. Which equals $\sin(45^\circ)$?

A. 1

B. $$\frac{\sqrt{3}}{2}$

C. $$\frac{\sqrt{2}}{2}$

D. $$\frac{1}{2}$

46. Which equals $\cos(\pi/4)$?

A. $$\frac{\sqrt{3}}{3}$

B. $$\frac{\sqrt{2}}{2}$

C. 1

D. $$\frac{1}{2}$

47. What is $\tan(30^\circ)$?

A. $$\sqrt{3}$

B. 1

C. $$\frac{1}{\sqrt{3}}$

D. $$\frac{\sqrt{3}}{3}$

48. What angle has $\sin(\theta) = \frac{1}{2}$?

A. $$90^\circ$

B. $$30^\circ$

C. $$60^\circ$

D. $$45^\circ$

49. In the right triangle, if the opposite side is 5 and the hypotenuse is 13, what is $\sin(\theta)$?

A. $$\frac{12}{13}$

B. $$\frac{5}{12}$

C. $$\frac{5}{13}$

D. $$\frac{12}{5}$

50. In the right triangle, if the opposite side is 4 and the adjacent side is 3, what is $\tan(\theta)$?

A. 0.75

B. 1.25

C. 1.33

D. 1.5

51. What angle has $\cos(\theta) = \frac{1}{2}$?

A. $$90^\circ$

B. $$45^\circ$

C. $$30^\circ$

D. $$60^\circ$

52. In the right triangle shown, if the adjacent side to angle $\theta$ is 5 and the hypotenuse is 13, what is $\cos(\theta)$?

A. $$12/13$

B. $$5/13$

C. $$13/5$

D. $$5/12$

53. In a right triangle, if the opposite side to angle $\theta$ is 15 and the adjacent side is 20, what is $\tan(\theta)$?

A. 3/5

B. 3/4

C. 4/3

D. 5/3

54. What is $\cos(60^\circ)$?

A. $$1$

B. $$\frac{\sqrt{3}}{2}$

C. $$\frac{\sqrt{2}}{2}$

D. $$\frac{1}{2}$

55. What is $\cos(\frac{\pi}{3})$?

A. 1

B. √3/2

C. 0

D. 1/2

56. What angle has $\sin(\theta) = \frac{\sqrt{3}}{2}$?

A. $$30^\circ$

B. $$60^\circ$

C. $$45^\circ$

D. $$90^\circ$

57. Which equals $\tan(90^\circ)$?

A. 0

B. Undefined

C. √3

D. 1

58. Which equals $\tan(60^\circ)$?

A. √3/2

B. 1

C. √3

D. 0

59. What angle $\theta$ (in degrees) satisfies $\sin(\theta)=\frac{\sqrt{2}}{2}$, where $0^\circ\le \theta \le 90^\circ$?

A. $$60^\circ$

B. $$30^\circ$

C. $$90^\circ$

D. $$45^\circ$

60. What is $\cos(60^\circ)$?

A. $$\frac{1}{2}$

B. $$\frac{\sqrt{3}}{2}$

C. $$1$

D. $$\frac{\sqrt{2}}{2}$

61. In a right triangle, the hypotenuse is $13$ and the side adjacent to an acute angle $\theta$ is $5$. What is $\cos(\theta)$?

A. $$\frac{5}{13}$

B. $$\frac{13}{5}$

C. $$\frac{5}{12}$

D. $$\frac{12}{13}$

62. Which equals $\tan(45^\circ)$?

A. $$\sqrt{3}$

B. $$\frac{1}{\sqrt{3}}$

C. 1

D. 0

63. What is $\tan(60^\circ)$?

A. $$\sqrt{3}$

B. $$\frac{\sqrt{3}}{3}$

C. 1

D. $$\frac{1}{\sqrt{3}}$

64. What is $\sin(60^\circ)$?

A. $$\frac{\sqrt{2}}{2}$

B. 1

C. $$\frac{1}{2}$

D. $$\frac{\sqrt{3}}{2}$

65. In the right triangle, if the adjacent side is 8 and the hypotenuse is 10, what is $\cos(\theta)$?

A. $$0.5$

B. $$0.75$

C. $$0.6$

D. $$0.8$

66. Which equals $\sin\left(\frac{\pi}{6}\right)$?

A. $$\frac{1}{2}$

B. $$\frac{\sqrt{2}}{2}$

C. $$\frac{\sqrt{3}}{2}$

D. $$0$

67. In a right triangle, the side adjacent to angle $\theta$ is $8$ and the hypotenuse is $17$. What is $\cos(\theta)$?

A. $$\frac{17}{8}$

B. $$\frac{8}{15}$

C. $$\frac{8}{17}$

D. $$\frac{15}{17}$

68. In the right triangle shown, the right angle is at $C$. The side lengths are $AC=5$, $BC=12$, and $AB=13$. Angle $\theta$ is at $A$. What is $\cos(\theta)$?

A. $$\frac{5}{13}$

B. $$\frac{5}{12}$

C. $$\frac{13}{12}$

D. $$\frac{12}{13}$

69. Which equals $\cos\left(\frac{\pi}{3}\right)$?

A. $$1$

B. $$\frac{\sqrt{3}}{2}$

C. $$\frac{\sqrt{2}}{2}$

D. $$\frac{1}{2}$

70. A right triangle has legs of lengths $5$ and $12$ (the legs meet at the right angle). Angle $\theta$ is adjacent to the side of length $12$ and has hypotenuse $13$. What is $\tan(\theta)$?

A. $$\frac{5}{12}$

B. $$\frac{12}{5}$

C. $$\frac{5}{13}$

D. $$\frac{13}{12}$

71. A right triangle has legs of lengths $9$ and $40$ (the legs meet at the right angle). Angle $\theta$ is opposite the side of length $9$. What is $\sin(\theta)$?

A. $$\frac{40}{41}$

B. $$\frac{41}{9}$

C. $$\frac{9}{41}$

D. $$\frac{9}{40}$

72. What is the radian measure of an angle of 135°?

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

B. $$\frac{4\pi}{3}$

C. $$\frac{3\pi}{4}$

D. $$\frac{5\pi}{4}$

73. For an angle $\theta$ in a right triangle, $\sin\theta = \frac{3}{5}$ and $\tan\theta = \frac{3}{4}$. What is the value of $\cos\theta$?

A. $$\frac{4}{3}$

B. $$\frac{5}{4}$

C. $$\frac{3}{5}$

D. $$\frac{4}{5}$

74. Which of the following equals $\cos\left(\frac{\pi}{3}\right)$?

A. $$\frac{\sqrt{2}}{2}$

B. $$\frac{1}{2}$

C. $$\frac{\sqrt{3}}{2}$

D. $$1$

75. What is $\sin(30^\circ)$?

A. $$\frac{1}{2}$

B. $$\frac{\sqrt{3}}{2}$

C. $$0$

D. $$\frac{\sqrt{2}}{2}$

76. In a right triangle, an acute angle $\theta$ has opposite side length $7$ and hypotenuse length $25$. What is $\sin(\theta)$?

A. $$\frac{24}{25}$

B. $$\frac{25}{7}$

C. $$\frac{7}{24}$

D. $$\frac{7}{25}$

77. What is $\tan(45^\circ)$?

A. $$\frac{\sqrt{2}}{2}$

B. $$1$

C. $$\sqrt{3}$

D. $$0$

78. In a right triangle, the legs are $6$ (opposite $\theta$) and $8$ (adjacent $\theta$). What is $\sin(\theta)$?

A. $$\frac{3}{5}$

B. $$\frac{5}{3}$

C. $$\frac{4}{5}$

D. $$\frac{3}{4}$

79. In a right triangle, an acute angle $\theta$ has opposite side length $9$ and adjacent side length $12$. What is $\tan(\theta)$?

A. $$\frac{3}{4}$

B. $$\frac{9}{15}$

C. $$\frac{4}{3}$

D. $$\frac{5}{4}$

80. In the right triangle shown, the right angle is at $A$. The side lengths are $AB=20$, $AC=21$, and $BC=29$. Angle $\theta$ is at $B$. What is $\cos(\theta)$?

A. $$\frac{29}{20}$

B. $$\frac{20}{21}$

C. $$\frac{20}{29}$

D. $$\frac{21}{29}$

81. In the right triangle shown, the right angle is at $C$. The side lengths are $AC=8$, $BC=15$, and $AB=17$. Angle $\theta$ is at $B$. What is $\sin(\theta)$?

A. $$\frac{8}{17}$

B. $$\frac{15}{17}$

C. $$\frac{8}{15}$

D. $$\frac{17}{8}$

82. What angle $\theta$ satisfies $\cos(\theta)=\frac{1}{2}$, where $\theta$ is a common acute angle?

A. $$60^\circ$

B. $$45^\circ$

C. $$0^\circ$

D. $$30^\circ$

83. In a right triangle, the side opposite angle $\theta$ is $7$ and the hypotenuse is $25$. What is $\sin(\theta)$?

A. $$\frac{25}{7}$

B. $$\frac{7}{24}$

C. $$\frac{24}{25}$

D. $$\frac{7}{25}$

84. In the right triangle shown, the right angle is at $B$. The side lengths are $AB=3$, $BC=4$, and $AC=5$. Angle $\theta$ is at $A$ (between $AB$ and $AC$). What is $\sin(\theta)$?

A. $$\frac{5}{3}$

B. $$\frac{5}{4}$

C. $$\frac{3}{5}$

D. $$\frac{4}{5}$

85. Which equals $\cos(30^\circ)$?

A. $$\frac{1}{2}$

B. $$\frac{\sqrt{2}}{2}$

C. $$0$

D. $$\frac{\sqrt{3}}{2}$

86. In a right triangle, the side opposite angle $\theta$ is $9$ and the side adjacent to $\theta$ is $12$. What is $\tan(\theta)$?

A. $$\frac{3}{5}$

B. $$\frac{3}{4}$

C. $$\frac{5}{3}$

D. $$\frac{4}{3}$

87. What is $\sin(30^\circ)$?

A. $$\sqrt{3}/2$

B. $$1/2$

C. $$1$

D. $$\sqrt{2}/2$

88. In a right triangle, if the opposite side to angle $\theta$ is 3 and the hypotenuse is 5, what is $\sin(\theta)$?

A. 3/5

B. 4/5

C. 5/4

D. 5/3

89. In the right triangle shown, if the opposite side to angle $\theta$ is 7 and the hypotenuse is 25, what is $\sin(\theta)$?

A. 7/25

B. 24/25

C. 25/24

D. 25/7

90. What is $\cos(0^\circ)$?

A. $$1$

B. $$\frac{\sqrt{3}}{2}$

C. $$0$

D. $$\frac{1}{2}$

91. In a right triangle, if the adjacent side to angle $\theta$ is 7 and the hypotenuse is 25, what is $\cos(\theta)$?

A. 7/25

B. 24/25

C. 25/24

D. 25/7

92. In the right triangle shown, if the adjacent side to angle $\theta$ is 4 and the hypotenuse is 5, what is $\cos(\theta)$?

A. 3/5

B. 4/5

C. 5/4

D. 5/3

93. What is $\sin(\frac{\pi}{2})$?

A. $$\frac{\sqrt{2}}{2}$

B. $$1$

C. $$\frac{1}{2}$

D. $$0$

94. What is $\cos(90^\circ)$?

A. $$\frac{1}{2}$

B. $$-1$

C. 0

D. 1

95. For an angle $\theta$ such that $0 < \theta < \dfrac{\pi}{2}$, it is known that $\sin(\theta) = \dfrac{3}{5}$. What is the value of $\cos(\theta) + \tan(\theta)$?

A. $$\dfrac{7}{5}$

B. $$\dfrac{31}{20}$

C. $$1$

D. $$2$

96. In triangle $ABC$, the right angle is at $B$. The length of $\overline{AB}$ is 8 units and the length of $\overline{BC}$ is 15 units. What is the value of $\tan C$?

A. $$\frac{8}{15}$

B. $$\frac{15}{8}$

C. $$\frac{15}{17}$

D. $$\frac{8}{17}$

97. In $\triangle ABC$, the length of side $a$ is 5, the length of side $b$ is 7, and the measure of $\angle C$ is $60°$. What is the length of side $c$?

A. $$\sqrt{74}$

B. $$\sqrt{39}$

C. $$\sqrt{109}$

D. $$8$

98. What is the maximum value of the trigonometric function $y = -3\sin(2x) + 4$?

A. 1

B. 3

C. 4

D. 7

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