Can someone please help me with the bottom question 3 2 poin

3. (2 points.) Find all solutions of the equation 3 sin 0 9 7 in the interval [0, 2m). Provide exact solutions and numerical approximation in radians rounded to three decimal places 41.810 4. (3 points.) Evaluate exact value of sin Tan (-2)+ Cos Show RTDs used in the computing.

Solution

sin( tan^-1(-2) + cos^-1(-2/3) )

let x = tan^-1(-2) ; y = cos^-1(-2/3)

tanx = -2 ; cosx = 1/sqrt5 ; sinx = -2/sqrt5

y = cos^-1(-2/3) ; cosy = -2/3

siny = sqrt5/3

sin(x +y) = sinxcosy +cosxsiny

sin( tan^-1(-2) + cos^-1(-2/3) ) = -2/sqrt5*(-2/3) + (1/sqrt5)*(sqrt5/3)

= [ 4+sqrt5 ]/3sqrt5