When (2.8) radians is approximately converted into degrees, which value is nearest?
Correct answer: C
\(2.8\times57.3^\circ\approx160.4^\circ\). For estimation take (1) radian as \(57.3^\circ\).
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Angles
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Medium · Level 69 · trigonometric-functions,angles,approx-radian
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- \(150.4^\circ\)
- \(155.8^\circ\)
- \(160.4^\circ\)
- \(168.2^\circ\)
Medium · Level 69 · trigonometric-functions,angles,approximation
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- (36.5^\circ)
- (43.0^\circ)
- (50.0^\circ)
- (57.3^\circ)
Medium · Level 69 · trigonometric-functions,angles,arc-angle
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- ( \frac{\pi}{2} ) radians
- ( \frac{2\pi}{3} ) radians
- ( \frac{3\pi}{2} ) radians
- ( \frac{4\pi}{3} ) radians
Medium · Level 69 · trigonometric-functions,angles,arc-length
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- (8\pi) cm
- (9\pi) cm
- (10\pi) cm
- (12\pi) cm
Medium · Level 69 · trigonometric-functions,angles,arc-length-degree
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- (8\pi) cm
- (10\pi) cm
- (12\pi) cm
- (14\pi) cm
Medium · Level 69 · trigonometric functions,angles,arc length,radian measure,circle radius
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- 18 cm
- 20 cm
- 24 cm
- 27 cm
Medium · Level 69 · trigonometric-functions,angles,sector-area
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- (60\pi) square cm
- (65\pi) square cm
- (70\pi) square cm
- (75\pi) square cm
Medium · Level 69 · trigonometric-functions,angles,sector-degree
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- (24\pi) square cm
- (27\pi) square cm
- (30\pi) square cm
- (36\pi) square cm
Medium · Level 69 · trigonometric-functions,angles,sector-angle
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- (2) radians
- (3) radians
- (4) radians
- (6) radians
Medium · Level 69 · trigonometric-functions,angles,sector-arc
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- (10) cm
- (12) cm
- (15) cm
- (18) cm
Medium · Level 69 · trigonometric-functions,angles,reference-angle
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- ( \frac{\pi}{5} )
- ( \frac{2\pi}{5} )
- ( \frac{3\pi}{10} )
- ( \frac{4\pi}{5} )
Medium · Level 69 · trigonometric-functions,angles,reference-radian
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- ( \frac{\pi}{7} )
- ( \frac{2\pi}{7} )
- ( \frac{3\pi}{7} )
- ( \frac{6\pi}{7} )
Medium · Level 69 · trigonometric-functions,angles,reference-principal
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- ( \frac{\pi}{6} )
- ( \frac{\pi}{3} )
- ( \frac{5\pi}{6} )
- ( \frac{7\pi}{6} )
Medium · Level 69 · trigonometric-functions,angles,reference-degree
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- (30^\circ)
- (45^\circ)
- (60^\circ)
- (90^\circ)
Medium · Level 69 · trigonometric-functions,angles,reference-angle
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- (30^\circ)
- (45^\circ)
- (60^\circ)
- (120^\circ)
Medium · Level 69 · trigonometric-functions,angles,axis-angle
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- (540^\circ)
- (720^\circ)
- (810^\circ)
- (990^\circ)
Medium · Level 69 · trigonometric-functions,angles,terminal-axis
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- (450^\circ)
- (630^\circ)
- (900^\circ)
- (1080^\circ)
Medium · Level 69 · trigonometric-functions,angles,radian-axis
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- Positive (x)-axis
- Positive (y)-axis
- Negative (x)-axis
- Negative (y)-axis
Medium · Level 69 · trigonometric-functions,angles,coterminal-rule
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- They are always complementary
- They are always supplementary
- They are coterminal
- They never have the same terminal side
Medium · Level 69 · trigonometric-functions,angles,axis-radian
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- ( \frac{\pi}{2} )
- ( \pi )
- ( \frac{3\pi}{2} )
- (2\pi)
When (0.75) radians is approximately converted into degrees, the value is closest to which option?
Correct answer: B
(0.75\times57.3^\circ\approx43.0^\circ). The same conversion factor applies for small radian values too.
View question detailsIf the radius of a circle is (21) cm and the arc is (14\pi) cm, what is the central angle in radians?
Correct answer: B
( \theta=\frac{s}{r}=\frac{14\pi}{21}=\frac{2\pi}{3} ). Use ( \theta=\frac{s}{r} ) to find the angle from arc length.
View question detailsIf (r=16) cm and ( \theta=\frac{5\pi}{8} ) radians, what will be the arc length?
Correct answer: C
(s=r\theta=16\times\frac{5\pi}{8}=10\pi) cm. When the angle is in radians, (s=r\theta) applies directly.
View question detailsWhat is the arc length made by an angle of (75^\circ) in a circle of radius (24) cm?
Correct answer: B
(75^\circ=\frac{5\pi}{12}), and (s=24\times\frac{5\pi}{12}=10\pi) cm. Convert degrees to radians before finding the arc.
View question detailsIf arc \(s=18\) cm and angle \( \theta=\frac{3}{4} \) radians, what is the radius?
Correct answer: C
When the angle is in radians, the arc-length formula is \(s=r\theta\). Therefore, \(r=\frac{s}{\theta}=\frac{18}{3/4}=18\times\frac{4}{3}=24\) cm. Hence, option C is correct. Option D may result from multiplying \(18\) by \(\frac{3}{4}\), but finding the radius requires division by \(\theta\). Exam tip: In arc-length questions, first check that the angle is expressed in radians.
View question detailsIf radius is (14) cm and central angle is ( \frac{5\pi}{7} ) radians, what is the area of the sector?
Correct answer: C
Area is ( \frac{1}{2}r^2\theta=\frac{1}{2}\times196\times\frac{5\pi}{7}=70\pi ). Use this formula directly with a radian angle.
View question detailsWhat will be the area of a sector with radius (9) cm and angle (120^\circ)?
Correct answer: B
(120^\circ=\frac{2\pi}{3}), and area is ( \frac{1}{2}\times81\times\frac{2\pi}{3}=27\pi ). Convert the degree angle into radians first.
View question detailsIf the sector area is (54) square cm and (r=6) cm, what is the central angle in radians?
Correct answer: B
From (54=\frac{1}{2}\times36\times\theta), ( \theta=3 ) radians. Isolate the unknown angle in the sector area formula.
View question detailsIf arc length is (20) cm and sector area is (150) square cm, what is the radius?
Correct answer: C
Sector area is ( \frac{1}{2}rs ), so (150=\frac{1}{2}\times r\times20) gives (r=15). When arc length is given, ( \frac{1}{2}rs ) is useful.
View question detailsWhat is the reference angle of an angle ( \theta=\frac{3\pi}{5} )?
Correct answer: B
( \frac{3\pi}{5} ) lies in the second quadrant, and the reference angle is ( \pi-\frac{3\pi}{5}=\frac{2\pi}{5} ). In the second quadrant use ( \pi-\theta ).
View question detailsWhat is the reference angle of ( \theta=\frac{8\pi}{7} )?
Correct answer: A
( \frac{8\pi}{7} ) lies in the third quadrant, and ( \frac{8\pi}{7}-\pi=\frac{\pi}{7} ). In the third quadrant use ( \theta-\pi ).
View question detailsAfter finding the principal coterminal angle of ( \theta=\frac{13\pi}{6} ), what will be the reference angle?
Correct answer: A
( \frac{13\pi}{6}-2\pi=\frac{\pi}{6} ), and it is in the first quadrant. First find the principal angle and then the reference angle.
View question detailsWhat will be the reference angle of (300^\circ)?
Correct answer: C
(300^\circ) lies in the fourth quadrant, and (360^\circ-300^\circ=60^\circ). In the fourth quadrant use (360^\circ-\theta).
View question detailsWhich is the reference angle of (240^\circ)?
Correct answer: C
(240^\circ) lies in the third quadrant, and (240^\circ-180^\circ=60^\circ). In the third quadrant subtract (180^\circ).
View question detailsWhich angle has its terminal side on the positive (x)-axis?
Correct answer: B
(720^\circ=2\times360^\circ), so its terminal side lies on the positive (x)-axis. Multiples of (360^\circ) return to this axis.
View question detailsWhich angle gives a terminal side on the negative (y)-axis?
Correct answer: B
(630^\circ-360^\circ=270^\circ), and (270^\circ) lies on the negative (y)-axis. First find the coterminal angle.
View question detailsOn which axis will the terminal side of ( \frac{15\pi}{2} ) radians lie?
Correct answer: D
( \frac{15\pi}{2}-6\pi=\frac{3\pi}{2} ), and ( \frac{3\pi}{2} ) lies on the negative (y)-axis. Subtract multiples of (2\pi) to identify the axis.
View question detailsIf the difference between two angles is (1080^\circ), what is the correct statement about them?
Correct answer: C
(1080^\circ=3\times360^\circ), so such angles are coterminal. If the difference is a multiple of (360^\circ), the terminal side is the same.
View question detailsIf the terminal side of ( \theta ) lies on the negative (x)-axis, what can be the value of ( \theta ) between (0) and (2\pi)?
Correct answer: B
The angle on the negative (x)-axis is ( \pi ) radians. Axis angles are not placed in quadrants.
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