If sin α = 0.407 sin α = 0.407 and sin β = 0.982 sin β = 0.982 with both angles’ terminal rays in Quadrant-I, find the values of

Question

If  sinα=0.407  and  sinβ=0.982  with both angles’ terminal rays in Quadrant-I, find the values of 

(a)

cos(α−β)=_____

(B)

sin(β−α)=_____

Answer 1

sinA =.407 sinB =.982 use an inverse trig function on a calculator

A= 24.017 degrees cosA = .913, cosB = .189

B = 79.113

A-B = -55.096

cos(A-B) - cos(-55.096) = 0.572

sin(B-A) = sin55.096 = 0.820

use the difference formulas

cos(A-B) = cosAcosB + sinAsinB = (.913)(.189) +(.407)(.982)= ..172+,400 = .572

cos(A-B) = approximately 0.572

sin(B-A) = sin55.096 = sinBcosA - sinAcosB= .982(.913) -.407(.189)= .897- .077= 0.820

sin(B-A) = approximately 0.820