Given cot α = 5/12 for α in Quadrant III and sec β = 7/5 for β in Quadrant IV. Find sin (α−β).

Question

Please show step by step in detail, thank you!

Answer 1

Cot=cos/sin. cotα=5/12; cotα=.417

α=247.36° (3rd qd)

Sec=1/cos=7/5; 7/7=1; 5/7=.714

cos=.714

β=44.415 or 315.585°; 4th qd

sin(α-β)=sin(247.36-315.59)=sin-68.23°sin=-.929

Answer 2

cot(a) = 5/12 --> sin(a) = -12/13, cos(a) = -5/13 since QIII

sec(b) = 7/5 --> cos(b) = 5/7 , sin(b) = -√24 / 7 = -2√6 / 7 , since QIV

sin(a-b) = sin(a)cos(b) - sin(b)cos(a)

= (-12/13)(5/7) - (-2√6 / 7)((-5/13)

= (-60 -10√6) / 91 ≈ -.92