If cos α = 0.929 cos α = 0.929 and cos β = 0.632 cos β = 0.632.

Question

If  cosα=0.929  and  cosβ=0.632 with both angles’ terminal rays in Quadrant-I, find the values of 

(a)

cos(β−α)= ______

(B)

sin(β−α)= ______

Answer 1

cosA = .929

A = 21.721 degrees

sinA = .370

cosB =.632 .

B = 50.802

sinB = .775

B-A = 29.081

cos(B-A) = cos 29.081=.874

sin(B-A) = sin29.081 = .486

or use difference trig formulas

cos(B-A) = cosBcosA + sinBsinA = .632(.929) + .775(.370) = .587+ .287=.874

cos(B-A)= 0.874

sin(B-A)= sinBcosA - sinAcosB = .775(.929)- .370(.632) = .720-.234 = .486

sin(B-A) = 0.486

Answer 2

Use the Pythagorean Identity to find the values of the sines:

sin²(α) + cos²(α) = 1

sin(α) = (1 - cos²(α))^1/2

Similarly, sin(β) = (1 - cos²(β))^1/2

Plug in the given values for the cosines to find the values for the sines. Now apply the difference of angles formulas:

cos(β-α) = cos(α)cos(β) + sin(β)sin(α)

sin(β-α) = sin(β)cos(α) - sin(α)sin(β)