solution for question 41 43 45 47 51 use a calculator to sol

use a calculator to solve each equation on the interval 0 lessthanorequalto theta 3/2 on the interval [-2 pi, 4 pi] Graph f(x) = 3 sin (2x) + 2 and g(x) = 7/2 on same Cartesian plane for the interval 0, pi]. Solve f(x) = g(x) on the interval [0, pi] and label points of intersection on the graph drawn in part. Solve f(x) > g(x) on the interval [0, pi]. Shade the region bounded by f(x) = 3 sin (2x) and g(x) = 7/2 between the two points found in part on the graph drawn in part(a). Graph f(x) = 2 cos x/2 + 3 and g(x) = 4 on the same Cartesian plane for the interval 0, 4 pi]. Solve f(x) = g(x) on the interval [0, 4 pi] and label points of intersection on the graph drawn in part. Solve f(x)

Solution

41

sin ( ) = 0.4

==> sin ( ) = 2/5

for range 0 < =   <= 2

= - arcsin( 2/5) , = arcsin( 2/5)

= - 0.41152 ,    = 0.41152

( 43 )

tan = 5

for range 0 < =    <= 2

= + arctan( 2/5) , = arctan( 5)

= + 1.37340 ,     = 1.37340

( 45 )

cos( ) = -0.9

==> cos( ) = -9/10

for range 0 < =   <= 2

= 2 - arccos(-9/10) , = arccos(-9/10)

= - 2.69057 ,     = 2.69057

( 47 )

sec() =-0.2

==> sec( ) = -1/5

for range 0 < =   <= 2

No solutios for belongs to ( epsilon) R

( 51 )

3 sin() - 2 =0

sin() = 2/3

for range 0 < =   <= 2

= - arcsin( 2/3) , = arcsin( 2/3)

= - 0.72973 ,     = 0.72973