Convert the angle to D degree M S form Round the answer to t

Convert the angle to D degree M\' S\" form. Round the answer to the nearest second. 86.79 degree If r = 5 meters, s = 8 meters and s denotes the length of the arc of a circle of radius r subtended by the central angle theta, find theta in f degrees. A water wheel has a radius of 10 feet. The wheel is rotating at 5 revolutions per minute. Find the linear speed of the water. Find the exact value of csc 2 pi/3 sec pi/4. p(3, -2)is a point on the circle corresponding to a real number t. Find the values of the trigonometric functions at t.If sin theta = 2/3 and cos theta

Solution

1) 86.70 deg to deg, minute and sec

86 deg ; 0.70*60 = 42 minute

So, 86.70 deg = 86 deg 42 min 0 sec

2) r = 5 mt ; s = 8 mt

theta = arc length/deg = 8/5 = 1.6 rad

In degrees , theta = 91.67 deg

4) csc2pi/3 + secpi/4

1/sin2pi/3 + 1/cospi/4

1/sin(pi -pi/3) + 1/cospi/4

1/sinpi/3 + 1/cospi/4

2/sqrt3 + sqrt2

=(2+ sqrt6)/sqrt3