(4) Addition and Difference: Trigonometric

Question

Given: sin a = -3/5, a is a third quadrant angle, and tan b = -7/24, b is a second-quadrant angle; find sun(a + b)

Answer 1

sina=-3/5, cosa=-4/5, it's a 3-4-5 right triangle

tanb=-7/24, sinb =7/25, cosb = -24/25, it's a 7-24-25 right triangle

sin(a+b)= sinacosb+ cosasinb =(-3/5)(-24/25)+ (-4/5)(7/25)

= (72 -28)/125

= 44/125

=exactly 0.352

check the answer:

a=about 36.87+180= 216.87 in Q3

b= about 180-16.26 =163.74, in Q2

a+b = 380.61 in Q1

sin380.61 =sin20.61 = 0.352