How would I go about solving this equation? If possible, please show how you found your answer.

Question

If cos α = 0.975 and sin β = 0.528 with both angles’ terminal rays in Quadrant-I, find the values of

B) sin (α + β)

B) cos (β - α)

Your answers should be accurate to 4 decimal places.

Answer 1

sin(a+b)= sinacosb +sinbcosa

cos(b-a)=cosacosb+sinasinb

sinb=.528

cosa= .975

sina= sqr(1-.975^2)= about .2222

cosb= sqr(1-.528^2)= about .8492

sin(a+b)=.2222(.8492)+.528(.975)

= .1887+.5148=.7035

b=sin^-1(.528)=31.87

a=cos^-1(.975)=12.84

31.87+12.84=44.71

sin44.71=.7035

cos(31.87-12.84)=cos19.03= .9453

Answer 2

cos ∝ = 0.975 ⇒ ∝ = 12.84º ⇒ sin ∝ = 0.2222

sin ß = 0.528 ⇒ ß = 31.87º ⇒ cos ß = 0.8492

Formulas for sum and difference of angles:

sin (∝ + ß) = sin (∝) cos (ß) + cos (∝) sin (ß) = (0.2222)(0.8492) + (0.9750)(0.5280) = 0.7035

cos(ß - ∝) = cos (ß) cos (∝) + sin (ß) sin (∝) = (0.8492)(0.9750) + (0.5280)(0.2222) = 0.9453

Check - Use actual sum of angles

∝ + ß = 12.84 + 31.87 = 44.71º ⇒ sin (44.71º) = 0.7035

ß - ∝ = 31.87 - 12.84 = 19.03º ⇒ cos (19.03º) = 0.9453