What is the degree measure of ( \frac{11\pi}{12} ) radians?
Correct answer: C
( \frac{11\pi}{12}\times \frac{180^\circ}{\pi}=165^\circ). First calculate (180^\circ\div 12).
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Angles
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Medium · Level 67 · trigonometric-functions,angles,standard-conversion
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- (150^\circ)
- (155^\circ)
- (165^\circ)
- (175^\circ)
Medium · Level 67 · trigonometric-functions,angles,radian-degree
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- (185^\circ)
- (190^\circ)
- (200^\circ)
- (195^\circ)
Medium · Level 67 · trigonometric-functions,angles,conversion
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- (255^\circ)
- (245^\circ)
- (260^\circ)
- (270^\circ)
Medium · Level 67 · trigonometric-functions,angles,radian-measure
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- (275^\circ)
- (285^\circ)
- (300^\circ)
- (295^\circ)
Medium · Level 67 · trigonometric-functions,angles,radian-to-degree
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- (335^\circ)
- (340^\circ)
- (345^\circ)
- (355^\circ)
Medium · Level 67 · trigonometric functions,angles,coterminal angles,standard angle,degree measure
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- \(60^\circ\)
- \(90^\circ\)
- \(150^\circ\)
- \(120^\circ\)
Medium · Level 67 · trigonometric functions,angles,coterminal angles,degree measure,positive angles
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- \(240^\circ\)
- \(300^\circ\)
- \(60^\circ\)
- \(120^\circ\)
Medium · Level 67 · trigonometric-functions,angles,principal-angle
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- (15^\circ)
- (30^\circ)
- (45^\circ)
- (75^\circ)
Medium · Level 67 · trigonometric-functions,angles,principal-coterminal
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- (30^\circ)
- (45^\circ)
- (120^\circ)
- (60^\circ)
Medium · Level 67 · trigonometric-functions,angles,radian-coterminal
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- ( \frac{\pi}{6} )
- ( \frac{5\pi}{6} )
- ( \frac{7\pi}{6} )
- ( \frac{11\pi}{6} )
Medium · Level 67 · trigonometric-functions,angles,negative-radian
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- ( \frac{3\pi}{4} )
- ( \frac{7\pi}{4} )
- ( \frac{\pi}{4} )
- ( \frac{5\pi}{4} )
Medium · Level 67 · trigonometric-functions,angles,principal-angle
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- ( \frac{\pi}{3} )
- ( \frac{4\pi}{3} )
- ( \frac{2\pi}{3} )
- ( \frac{5\pi}{3} )
Medium · Level 67 · trigonometric-functions,angles,radian-range
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- ( \frac{\pi}{3} )
- ( \frac{2\pi}{3} )
- ( \frac{4\pi}{3} )
- None except ( \frac{\pi}{3} )
Medium · Level 67 · trigonometric-functions,angles,coterminal-test
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- They are complementary angles
- They are coterminal angles
- They are supplementary angles
- They are opposite angles
Medium · Level 67 · trigonometric-functions,angles,quadrant-negative
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 67 · trigonometric-functions,angles,quadrant
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 67 · trigonometric-functions,angles,radian-quadrant
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 67 · trigonometric-functions,angles,quadrant-radian
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 67 · trigonometric-functions,angles,terminal-side
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- First quadrant
- Second quadrant
- Third quadrant
- Fourth quadrant
Medium · Level 67 · trigonometric-functions,angles,approximation
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- (45.3^\circ)
- (60.0^\circ)
- (90.0^\circ)
- (57.3^\circ)
What is obtained by converting ( \frac{13\pi}{12} ) radians into degrees?
Correct answer: D
( \frac{13\pi}{12}\times \frac{180^\circ}{\pi}=195^\circ). Remember ( \frac{\pi}{12}=15^\circ).
View question detailsWhich is the degree measure of ( \frac{17\pi}{12} ) radians?
Correct answer: A
( \frac{17\pi}{12}=17\times 15^\circ=255^\circ). Take ( \frac{\pi}{12}=15^\circ) for a quick solution.
View question detailsHow many degrees are ( \frac{19\pi}{12} ) radians?
Correct answer: B
( \frac{19\pi}{12}\times \frac{180^\circ}{\pi}=285^\circ). If the denominator is (12) multiply the numerator by (15^\circ).
View question detailsConvert ( \frac{23\pi}{12} ) radians into degrees.
Correct answer: C
( \frac{23\pi}{12}=23\times 15^\circ=345^\circ). Be careful with values close to (360^\circ).
View question detailsWhat is the coterminal angle of (840^\circ) between (0^\circ) and (360^\circ)?
Correct answer: D
Coterminal angles differ by an integral multiple of \(360^\circ\). Since \(840^\circ-2\times360^\circ=120^\circ\), the coterminal angle lying between \(0^\circ\) and \(360^\circ\) is \(120^\circ\). Although \(90^\circ\) may seem close, \(840^\circ-90^\circ=750^\circ\), which is not a multiple of \(360^\circ\). Exam tip: add or subtract multiples of \(360^\circ\) to bring an angle into the required interval.
View question detailsWhich is the positive coterminal angle of ( -780^\circ )?
Correct answer: B
Coterminal angles differ by an integral multiple of \(360^\circ\). Adding \(3\times360^\circ=1080^\circ\) to \(-780^\circ\) gives \(300^\circ\): \(-780^\circ+1080^\circ=300^\circ\). Hence, \(300^\circ\) is correct. \(240^\circ\) is not coterminal because \(240^\circ-(-780^\circ)=1020^\circ\), which is not a multiple of \(360^\circ\). Exam tip: Keep adding \(360^\circ\) to a negative angle until the least positive angle is obtained.
View question detailsWhat is the principal coterminal angle of (1125^\circ)?
Correct answer: C
(1125^\circ-1080^\circ=45^\circ). For the principal angle use the range from (0^\circ) to (360^\circ).
View question detailsWhat will be the principal coterminal angle of ( -1020^\circ )?
Correct answer: D
( -1020^\circ+1080^\circ=60^\circ ). Add a suitable multiple of (360^\circ) for large negative angles.
View question detailsWhat is the coterminal angle of ( \frac{25\pi}{6} ) between (0) and (2\pi)?
Correct answer: A
( \frac{25\pi}{6}-\frac{24\pi}{6}=\frac{\pi}{6} ). Subtract (2\pi) in radians to find the principal angle.
View question detailsWhat is the coterminal angle of ( -\frac{17\pi}{4} ) between (0) and (2\pi)?
Correct answer: B
( -\frac{17\pi}{4}+\frac{24\pi}{4}=\frac{7\pi}{4} ). Add multiples of (2\pi) to a negative radian angle.
View question detailsWhich is the principal coterminal angle of ( \frac{14\pi}{3} )?
Correct answer: C
( \frac{14\pi}{3}-\frac{12\pi}{3}=\frac{2\pi}{3} ). Write (2\pi=\frac{6\pi}{3}) and subtract.
View question detailsWhat will be the angle between (0) and (2\pi) for ( -\frac{11\pi}{3} )?
Correct answer: A
( -\frac{11\pi}{3}+\frac{12\pi}{3}=\frac{\pi}{3} ). Keeping the same denominator makes adding (2\pi) easy.
View question detailsWhich statement about (725^\circ) and (5^\circ) is correct?
Correct answer: B
(725^\circ-5^\circ=720^\circ=2\times 360^\circ) so they are coterminal. If the difference is a multiple of (360^\circ) the angles are coterminal.
View question detailsIn which quadrant will the terminal side of ( -220^\circ ) lie?
Correct answer: B
( -220^\circ+360^\circ=140^\circ ) and (140^\circ) lies in the second quadrant. First convert a negative angle to a positive coterminal angle.
View question details( -310^\circ ) is coterminal with an angle in which quadrant?
Correct answer: A
( -310^\circ+360^\circ=50^\circ ) and (50^\circ) lies in the first quadrant. The coterminal angle gives the quadrant easily.
View question detailsIn which quadrant does ( \frac{8\pi}{5} ) radians lie?
Correct answer: D
( \frac{8\pi}{5}=288^\circ ) so it lies in the fourth quadrant. Convert radians to degrees when needed.
View question detailsIn which quadrant is ( \frac{7\pi}{10} ) radians?
Correct answer: B
( \frac{7\pi}{10}=126^\circ ) and it lies between (90^\circ) and (180^\circ). Check the interval to decide the quadrant.
View question detailsIn which quadrant is the terminal side of ( \frac{11\pi}{10} ) radians?
Correct answer: C
( \frac{11\pi}{10}=198^\circ ) so it is in the third quadrant. The interval between (180^\circ) and (270^\circ) is the third quadrant.
View question detailsIf (1) radian is written approximately in degrees then which is the nearest correct value?
Correct answer: D
(1) radian is ( \frac{180^\circ}{\pi} \approx 57.3^\circ ). Use ( \pi\approx 3.14 ) for approximation.
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