What is the radian measure of (37.5^\circ)?
Correct answer: B
(37.5^\circ=\frac{37.5\pi}{180}=\frac{5\pi}{24}). You can also treat (37.5^\circ) as ( \frac{75^\circ}{2} ).
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Angles
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Medium · Level 68 · trigonometric-functions,angles,radian-conversion
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- ( \frac{\pi}{8} ) radians
- ( \frac{5\pi}{24} ) radians
- ( \frac{7\pi}{24} ) radians
- ( \frac{\pi}{5} ) radians
Medium · Level 68 · trigonometric functions, angles, coterminal angles, degree measure, class 11 mathematics
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- \(-150^\circ\)
- \(150^\circ\)
- \(-210^\circ\)
- \(30^\circ\)
Medium · Level 68 · trigonometric-functions,angles,degree-to-radian
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- ( \frac{7\pi}{4} ) radians
- ( \frac{5\pi}{2} ) radians
- ( \frac{11\pi}{6} ) radians
- ( \frac{9\pi}{4} ) radians
Medium · Level 68 · trigonometric-functions,angles,radian-to-degree
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- (67.5^\circ)
- (60^\circ)
- (75^\circ)
- (82.5^\circ)
Medium · Level 68 · trigonometric-functions,angles,degrees
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- (35^\circ)
- (37.5^\circ)
- (40^\circ)
- (45^\circ)
Medium · Level 68 · trigonometric-functions,angles,negative-radian
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- (210^\circ)
- (-180^\circ)
- (-210^\circ)
- (-240^\circ)
Medium · Level 68 · trigonometric-functions,angles,standard-conversion
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- (282.5^\circ)
- (270^\circ)
- (300^\circ)
- (292.5^\circ)
Medium · Level 68 · trigonometric functions,angles,coterminal angles,degree measure,angle reduction
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- \(265^\circ\)
- \(255^\circ\)
- \(275^\circ\)
- \(285^\circ\)
Medium · Level 68 · trigonometric-functions,angles,negative-coterminal
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- (70^\circ)
- (80^\circ)
- (90^\circ)
- (100^\circ)
Medium · Level 68 · trigonometric-functions,angles,principal-angle
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- (80^\circ)
- (90^\circ)
- (100^\circ)
- (120^\circ)
Medium · Level 68 · trigonometric-functions,angles,principal-coterminal
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- (350^\circ)
- (20^\circ)
- (30^\circ)
- (10^\circ)
Medium · Level 68 · trigonometric-functions,angles,radian-coterminal
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- ( \frac{5\pi}{4} )
- ( \frac{3\pi}{4} )
- ( \frac{7\pi}{4} )
- ( \frac{\pi}{4} )
Medium · Level 68 · trigonometric-functions,angles,negative-radian
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- ( \frac{\pi}{6} )
- ( \frac{5\pi}{6} )
- ( \frac{7\pi}{6} )
- ( \frac{11\pi}{6} )
Medium · Level 68 · trigonometric-functions,angles,principal-radian
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- ( \frac{4\pi}{3} )
- ( \frac{\pi}{3} )
- ( \frac{5\pi}{3} )
- ( \frac{2\pi}{3} )
Medium · Level 68 · trigonometric-functions,angles,radian-range
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- ( \frac{\pi}{8} )
- ( \frac{5\pi}{8} )
- ( \frac{7\pi}{8} )
- ( \frac{15\pi}{8} )
Medium · Level 68 · trigonometric-functions,angles,quadrant-negative
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 68 · trigonometric-functions,angles,quadrant
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 68 · trigonometric-functions,angles,radian-quadrant
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 68 · trigonometric-functions,angles,terminal-side
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 68 · trigonometric-functions,angles,fourth-quadrant
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Which of the following angles is an example of a coterminal angle of \(210^\circ\)?
Correct answer: A
Coterminal angles have the same initial and terminal sides, so their difference is a multiple of \(360^\circ\). Since \(210^\circ-360^\circ=-150^\circ\), option A is correct. The difference between \(210^\circ\) and \(150^\circ\) is only \(60^\circ\). Exam tip: add or subtract \(360^\circ\) to test coterminal angles.
View question detailsWhich is the radian form of (405^\circ)?
Correct answer: D
(405^\circ=\frac{405\pi}{180}=\frac{9\pi}{4}). Use the same rule even for angles greater than (360^\circ).
View question detailsWhat do we get by converting ( \frac{3\pi}{8} ) radians into degrees?
Correct answer: A
( \frac{3\pi}{8}\times \frac{180^\circ}{\pi}=67.5^\circ). Divide (180^\circ) by (8) and then multiply.
View question detailsHow many degrees are equal to ( \frac{5\pi}{24} ) radians?
Correct answer: B
( \frac{5\pi}{24}\times \frac{180^\circ}{\pi}=37.5^\circ). If the denominator is (24), calculate (180^\circ\div 24).
View question detailsWhat is the degree measure of ( -\frac{7\pi}{6} ) radians?
Correct answer: C
( -\frac{7\pi}{6}\times \frac{180^\circ}{\pi}=-210^\circ). The negative sign in radians remains in degrees.
View question detailsConvert ( \frac{13\pi}{8} ) radians into degrees.
Correct answer: D
( \frac{13\pi}{8}\times \frac{180^\circ}{\pi}=292.5^\circ). Remember ( \frac{\pi}{8}=22.5^\circ ).
View question detailsWhat is the coterminal angle of (985^\circ) between (0^\circ) and (360^\circ)?
Correct answer: A
To find a coterminal angle, subtract a multiple of \(360^\circ\) from the given angle. \(985^\circ-2\times360^\circ=985^\circ-720^\circ=265^\circ\). Therefore, \(265^\circ\) is the coterminal angle of \(985^\circ\) between \(0^\circ\) and \(360^\circ\). The other options do not differ from \(985^\circ\) by a whole multiple of \(360^\circ\). Exam tip: reduce an angle modulo \(360^\circ\) to obtain its standard coterminal angle.
View question detailsWhich is the coterminal angle of ( -1000^\circ ) between (0^\circ) and (360^\circ)?
Correct answer: B
( -1000^\circ+1080^\circ=80^\circ ). Add multiples of (360^\circ) for large negative angles.
View question detailsWhat will be the principal angle of (1540^\circ)?
Correct answer: C
(1540^\circ-1440^\circ=100^\circ). The principal angle is usually taken between (0^\circ) and (360^\circ).
View question detailsWhat is the principal coterminal angle of ( -1430^\circ )?
Correct answer: D
( -1430^\circ+1440^\circ=10^\circ ). Adding the nearest larger multiple of (360^\circ) is easy.
View question detailsWhat is the coterminal angle of ( \frac{29\pi}{4} ) between (0) and (2\pi)?
Correct answer: A
( \frac{29\pi}{4}-\frac{24\pi}{4}=\frac{5\pi}{4} ). In radians subtract (2\pi=\frac{8\pi}{4}).
View question detailsWhat is the coterminal angle of ( -\frac{19\pi}{6} ) between (0) and (2\pi)?
Correct answer: B
( -\frac{19\pi}{6}+\frac{24\pi}{6}=\frac{5\pi}{6} ). Add multiples of (2\pi) to a negative radian angle.
View question detailsWhich is the principal coterminal angle of ( \frac{31\pi}{3} )?
Correct answer: B
( \frac{31\pi}{3}-\frac{30\pi}{3}=\frac{\pi}{3} ). Subtract a multiple of (2\pi=\frac{6\pi}{3}).
View question detailsWhat is the angle between (0) and (2\pi) for ( -\frac{25\pi}{8} )?
Correct answer: C
( -\frac{25\pi}{8}+\frac{32\pi}{8}=\frac{7\pi}{8} ). Keeping the same denominator is a safe method while adding (2\pi).
View question detailsIn which quadrant will the terminal side of ( -250^\circ ) lie?
Correct answer: B
( -250^\circ+360^\circ=110^\circ ) and (110^\circ) lies in the second quadrant. First find the positive coterminal angle.
View question details( -710^\circ ) gives a coterminal angle in which quadrant?
Correct answer: A
( -710^\circ+720^\circ=10^\circ ), so the terminal side lies in the first quadrant. Add multiples of (360^\circ) to a large negative angle.
View question detailsIn which quadrant does ( \frac{9\pi}{7} ) radians lie?
Correct answer: C
( \pi<\frac{9\pi}{7}<\frac{3\pi}{2} ), so it lies in the third quadrant. Identify the quadrant directly from radian intervals.
View question detailsIn which quadrant is the terminal side of ( \frac{13\pi}{9} ) radians?
Correct answer: C
( \pi<\frac{13\pi}{9}<\frac{3\pi}{2} ), so it is in the third quadrant. The interval between ( \pi ) and ( \frac{3\pi}{2} ) is the third quadrant.
View question detailsIn which quadrant does ( \frac{17\pi}{9} ) radians lie?
Correct answer: D
( \frac{3\pi}{2}<\frac{17\pi}{9}<2\pi ), so it lies in the fourth quadrant. Compare radians by using a common denominator.
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