If a is a quadrant 1 angle, such that sina=2/5 and b is a quadrant 3 angle, such that tanb=1, find sin(a+b) and cos(a+b) and the quadrant in with a+b lies in. find sin2a. * show work*

Answers: sin(A+B)=, cos(A+B)=, A+B=Quadrant 3, sin(2A)=

NOTES:

sin A =      ⇒    cos A =

since tan B = 1 and is in Quadrant 3, then

sin B =    and  cos B =

SIN (A + B):

sin (A + B) = (sin A * cos B) + (cos A * sin B)

                 = ()() + ()()

                  = +

                  =

COS (A + B):

cos (A + B) = (cos A * cos B) - (sin A * sin B)

                  = ()() - ()()

                  = -

                  =

SIN 2A:

sin (A + A) = 2 (sin A * cos A)

                 = 2 ()()

                 =

A + B:

sin A =

    A = sin⁻¹

    A = 23.57°

tan B = 1

      B = tan⁻¹(1)

      B = 45°  

         = 45° + 180° in Quadrant 3

         = 225°

A + B = 23.6° + 225°

         = 248.6°  which lies in Quadrant 3

do i do it on a graph?

step-by-step explanation: