If (\frac{3\pi}{5}) radians is converted into degrees, what is the angle?
Correct answer: B
(\frac{3\pi}{5}\times\frac{180^\circ}{\pi}=108^\circ). In exams, cancel (\pi) before multiplying.
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Angles
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Hard · Level 68 · trigonometry angles conversion hard class11
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- (96^\circ)
- (108^\circ)
- (120^\circ)
- (135^\circ)
Hard · Level 68 · trigonometry angles coterminal hard class11
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- (2)
- (3)
- (4)
- (8)
Hard · Level 68 · trigonometry angles clock hard class11
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- (\frac{17\pi}{30})
- (\frac{17\pi}{60})
- (\frac{17\pi}{15})
- (\frac{34\pi}{45})
Hard · Level 68 · trigonometry angles degree minute hard class11
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- (11.15^\circ)
- (11.20^\circ)
- (11.25^\circ)
- (11.30^\circ)
Hard · Level 68 · trigonometry angles quadrant hard class11
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Hard · Level 68 · trigonometry angles reference hard class11
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- \(145^\circ\)
- \(215^\circ\)
- \(325^\circ\)
- \(305^\circ\)
Hard · Level 68 · trigonometry angles reference hard class11
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- (158^\circ)
- (202^\circ)
- (338^\circ)
- (292^\circ)
Hard · Level 68 · trigonometry angles quadrant hard class11
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Hard · Level 68 · trigonometry angles minute radian hard class11
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- (\frac{\pi}{10800})
- (\frac{\pi}{3600})
- (\frac{\pi}{21600})
- (\frac{\pi}{648000})
Hard · Level 68 · trigonometry angles second radian hard class11
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- (\frac{\pi}{10800})
- (\frac{\pi}{21600})
- (\frac{\pi}{324000})
- (\frac{\pi}{648000})
Hard · Level 68 · trigonometry angles principal hard class11
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- (\frac{\pi}{3})
- (\frac{2\pi}{3})
- (\frac{4\pi}{3})
- (\frac{5\pi}{3})
Hard · Level 68 · trigonometry angles coterminal hard class11
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- (\frac{\pi}{4})
- (\frac{3\pi}{4})
- (\frac{5\pi}{4})
- (\frac{7\pi}{4})
Hard · Level 68 · trigonometry angles arc length hard class11
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- (2\pi) cm
- (3\pi) cm
- (4\pi) cm
- (5\pi) cm
Hard · Level 68 · trigonometry angles sector area hard class11
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- (20\pi) square cm
- (30\pi) square cm
- (40\pi) square cm
- (50\pi) square cm
Hard · Level 68 · trigonometry angles rotation hard class11
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- (45\pi)
- (60\pi)
- (90\pi)
- (180\pi)
Hard · Level 68 · trigonometry angles quadrant hard class11
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Hard · Level 68 · trigonometry angles reference hard class11
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- (\frac{\pi}{8})
- (\frac{3\pi}{8})
- (\frac{5\pi}{8})
- (\frac{7\pi}{8})
Hard · Level 68 · trigonometry angles degree minute hard class11
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- (\frac{53\pi}{72})
- (\frac{47\pi}{72})
- (\frac{41\pi}{72})
- (\frac{59\pi}{72})
Hard · Level 68 · trigonometry angles principal hard class11
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- (80^\circ)
- (100^\circ)
- (260^\circ)
- (300^\circ)
Hard · Level 68 · trigonometry angles conversion hard class11
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- (95)
- (100)
- (105)
- (110)
If the difference between two coterminal angles is (8\pi), how many complete rotations apart are they?
Correct answer: C
One complete rotation is (2\pi), so (\frac{8\pi}{2\pi}=4). In exams, remember that a full rotation in radians is (2\pi).
View question detailsThrough how many radians does the minute hand of a clock rotate in (17) minutes?
Correct answer: A
The minute hand rotates (2\pi) in (60) minutes, so in (17) minutes it rotates (\frac{17\pi}{30}). In exams, use time ratio to find the angle.
View question detailsIf an angle is (11^\circ 15'), what is its decimal degree measure?
Correct answer: C
(15'=\frac{15}{60}^\circ=0.25^\circ), so the total is (11.25^\circ). In exams, divide minutes by (60).
View question detailsIn which quadrant does the angle (2.35) radians lie?
Correct answer: B
Since (\frac{\pi}{2}<2.35<\pi), the angle lies in the second quadrant. In exams, compare radians with (\frac{\pi}{2}), (\pi), and (\frac{3\pi}{2}).
View question detailsIf \(\theta\) lies in the third quadrant and its reference angle is \(35^\circ\), what is \(\theta\)?
Correct answer: B
In the third quadrant, the angle is \(180^\circ+\alpha\). So \(180^\circ+35^\circ=215^\circ\).
View question detailsIf (\theta) lies in the fourth quadrant and the reference angle is (22^\circ), what is the principal angle?
Correct answer: C
In the fourth quadrant, the principal angle is (360^\circ-\alpha). In exams, treat the reference angle as the distance from the axis.
View question detailsIn which quadrant will the terminal side of (\frac{19\pi}{6}) radians lie?
Correct answer: B
(\frac{19\pi}{6}-2\pi=\frac{7\pi}{6}), which lies in the third quadrant. In exams, reduce the angle before identifying the quadrant.
View question detailsIf the radian measure of (1^\circ) is (\frac{\pi}{180}), what is the radian measure of (1')?
Correct answer: A
(1'=\frac{1}{60}^\circ), so its radian measure is (\frac{\pi}{180\times60}). In exams, first convert minutes into degrees.
View question detailsWhich is the correct radian measure of (1'')?
Correct answer: D
(1''=\frac{1}{3600}^\circ), so the radian measure is (\frac{\pi}{180\times3600}). In exams, do not forget to convert seconds into degrees.
View question detailsIf an angle is (\frac{31\pi}{3}), what is its principal angle?
Correct answer: A
Remove (\frac{30\pi}{3}=10\pi) from (\frac{31\pi}{3}) to get (\frac{\pi}{3}). In exams, remove the nearest multiple of (2\pi).
View question detailsIf (\theta=-\frac{17\pi}{4}), what is the coterminal angle between (0) and (2\pi)?
Correct answer: D
(-\frac{17\pi}{4}+6\pi=\frac{7\pi}{4}). In exams, add multiples of (2\pi) to a negative angle.
View question detailsIf a sector has radius (9) cm and angle (80^\circ), what is the arc length?
Correct answer: C
(80^\circ=\frac{4\pi}{9}) radians and (s=9\times\frac{4\pi}{9}=4\pi). In exams, convert degrees into radians first.
View question detailsWhat is the area of a sector with radius (12) cm and angle (150^\circ)?
Correct answer: B
(150^\circ=\frac{5\pi}{6}) and (A=\frac{1}{2}\times144\times\frac{5\pi}{6}=60\pi). The correct area should be (60\pi).
View question detailsIf a wheel makes (45) revolutions, through how many radians does it rotate?
Correct answer: C
One revolution is (2\pi) radians, so (45) revolutions are (90\pi) radians. In exams, multiply revolutions by (2\pi).
View question detailsIf an angle is (3.9) radians, in which quadrant is it located?
Correct answer: C
Since (\pi<3.9<\frac{3\pi}{2}), the angle is in the third quadrant. In exams, compare with (\pi\approx3.14) and (\frac{3\pi}{2}\approx4.71).
View question detailsIf (\theta=\frac{29\pi}{8}), what is the reference angle of (\theta)?
Correct answer: B
(\frac{29\pi}{8}-2\pi=\frac{13\pi}{8}), which lies in the fourth quadrant? The reference angle is (\frac{3\pi}{8}). In exams, reduce first and then find the distance from the nearest (x)-axis.
View question detailsIf (132^\circ 30') is converted into radians, what is the correct form?
Correct answer: A
(132^\circ 30'=132.5^\circ=\frac{265}{2}^\circ), so radians are (\frac{265\pi}{360}=\frac{53\pi}{72}). In exams, convert minutes into decimal degrees.
View question detailsIf the principal angle of (\theta) is (280^\circ), what is the principal angle of (-\theta)?
Correct answer: A
(-280^\circ+360^\circ=80^\circ). In exams, add (360^\circ) to make a negative angle positive.
View question detailsIf (a^\circ) and (\frac{7\pi}{12}) radians represent the same angle, what is (a)?
Correct answer: C
(\frac{7\pi}{12}\times\frac{180^\circ}{\pi}=105^\circ). In exams, cancel (\pi) while converting radians to degrees.
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