l e 10 points per problem for a total of 10 problems L Find

l e 10 points per problem for a total of 10 problems L. Find the exact value of each expression a.) cos\"(-2)- show all steps of your work to gain any cred: Please 2. cos ( a. b.) sin-1+) 2 3. Find the exact value ofsn(-30°).

Solution

1 a) cos^-1( -1/2)

Since range of y = cos^-1(x) is between 0<= y<= 180

So, cos^-1( -1/2) = pi -pi/3 = 2pi/3

b) sin^-1(1/2)

range of y = sin^-1(x) is between -pi/2 <= y< = pi/2

y = sin^-1(1/2) = pi/6

2. a) cos(sin^-1(2/3))

Let y = sin^-1(2/3)

siny = 2/3

cosy = sqrt( 1- 4/9) = sqrt(5)/3

y = cos^-1( sqrt(5)/3)

cos(sin^-1(2/3)) = cos( cos^-1( sqrt(5)/3) ) = sqrt(5)/3

b) sin^-1(sin(-pi/5) ) = -pi/5

4. sinx cosx[ 2tanx +2cotx ]

sinxcosx(2sinx/cosx) + sinxcosx(2cosx/sinx)

sinx(2sinx) + cosx(2cosx)

2(sin^2x +cos^2x)

=2*1 =2