(3) 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 cos(a + b)

Answer 1

sin(a+b)=exactly 0.352 = 44/125 (from your other posted problem)

cos(a+b)= exactly .936 as a+b= about 380.61 degrees

cos(a+b)=cosacosb - sinasinb

=(-4/5)(-24/25)- (-3/5)(7/25)

= 96/125 + 21/125

= 117/125

= exactly .936