fertheexfsuc Ces3t on ces3 C Solution1 cos3t cos2tt use for

fer-the-exfsuc. Ces3t on ces3 C

Solution

1) cos(3t) = cos(2t+t)

use formula : cos(a+b) = cosa*cosb - sina*sinb

cos(3t) = cos(2t+t) = cos2tcost - sin2tsint

= ( 2cos^2t -1)cost - 2sin^2tcost

= 2cos^3t - cost - 2(1-cos^2t)cost

= 2cos^3t - cost - 2cost + 2cos^3t

= 4cos^3t - 3cost    ( in terms of cost)

2) In which quadrant we have to solve for

3) 8sin^2a + 9 = 10

sin^2a = 1/8

sina = +/- 1/2sqrt2

a = sin^-1(1/2sqrt2)

= 0.36 , pi -0.36

a= 0.36 ; a = 2.78 radians

a = - sin^-1(1/2sqrt2)

= pi +0.36 , 2pi -0.36

a= 3.50 , 5.92 radians

a = -sin^-1(1/2sqrt2)