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Find the degree measure corresponding to the following radian measures (Use π =)
(i) (ii) - (iii) c (iv) (-3)c (v) 11c (vi) 1c
Find the radian measure corresponding to the following degree measures:
(i) 3000 (ii) 350 (iii) -560 (iv)1350 (v) -3000
(vi) 70 30’ (vii) 1250 30’ (viii) -47o 30’
The difference between the two acute angles of a right-angled triangle is 2π/5 radians. Express the angles in degrees.
One angle of a triangle is grades, and another is degrees while the third is radians. Express all the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular:
(i) Pentagon (ii) Octagon (iii) Heptagon (iv) Duodecagon.
The angles of a quadrilateral are in A.P., and the greatest angle is 1200. Express the angles in radians.
The angles of a triangle are in A.P., and the number of degrees in the least angle is to the number of degrees in the mean angle as 1:120. Find the angle in radians.
The angle in one regular polygon is to that in another as 3:2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
The number of sides of two regular polygons is 5:4 and the difference between their angle is 90. Find the number of sides of the polygons.
A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 250 at a distance of 40 meters?
Find the length which at a distance of 5280 m will subtend an angle of 1’ at the eye.
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm.
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
A railway train is traveling on a circular curve of 1500 meters radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31’.
Find the diameter of the Sun in km supposing that it subtends an angle of 32’ at the eye of an observer. Given that the distance of the Sun is 91 x 106 km.
If the arcs of the same length in two circles subtend angles 650 and 1100 at the center, find the ratio of their radii.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π = ).
Mark the correct alternative in the following:
If D, G and R denote respectively the number of degrees, grades and radians in an angle, then
If the angles of a triangle are in A.P., then the measure of one of the angles in radians is
The angle between the minute and hour hands of a clock at 8:30 is
At 3:40, the hour and minute hands of a clock are inclined at
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, then the ratio of the radii of the circles is
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of 3π/4 radian at the centre is