Answer Problem 7 on Answer Sheet 7 s 7 a A central angle of

Answer Problem 7 on Answer Sheet 7. (s) 7. a. A central angle of 140° subtends an arc of length 10 feet on a circle. Find the radius of the circle. b. Let cos 2/5 and tan t

Solution

a. s= r theta

s=10feet

theta=140degree=140pi/180=7pi/9radians

10=7r pi/10

r= 100/(7pi)=0.5feet

cos t=-2/5

tan t is negative means theta is in second quadrant where sin and csc are positive

sin t=sqrt(1-cos²t)= sqrt(1- 4/25)= sqrt21/5

sin(t+3pi/4) = sin t cos (3pi/4)+cos t sin(3pi/4) = (sqrt21/5)(-sqrt2/2)+(-2/5)(sqrt2/2)= (-sqrt2 /10)(sqrt21-2)

ii. sec (2t)= 1/cos(2t)=1/(2cos²t-1)= 1/(-17/25)= -(25/17)

iii. cos(11pi/6 -t) = cos (11pi/6)cos t+sin(11pi/6)sin t

=(sqrt3/2)(-2/5)-(-1/2)(sqrt21/5)

= -(2sqrt(3)+sqrt(21))/10