If sin alpha 35 and and sec beta 54 for a thirdquadrant an

If sin alpha = -3/5 and and sec beta = 5/4 for a third-quadrant angle a and a first-quadrant angle beta, find the following. sin(alpha + beta) tan(alpha + beta) the quadrant containing alpha + beta Quadrant I Quadrant II Quadrant III Quadrant IV

Solution

given sin =-3/5 , in Quadrant 3

cos =-((5²-3²))/5

cos =-4/5

given sec =5/4, in Quadrant 1

cos=1/sec =4/5

sin=((5²-4²))/5

sin=3/5

a)sin(+)=sincos +cossin

sin(+)=(-3/5)(4/5) +(-4/5)(3/5)

sin(+)=-24/25

cos(+)=coscos -sinsin

cos(+)=(-4/5)(4/5) - (-3/5)(3/5)

cos(+)=-7/25

b)tan(+)=sin(+)/cos(+)

tan(+)=(-24/25)/(-7/25)

tan(+)=24/7

c)(+) in Quadrant 3