Question

If sinx=(-15)/17 with π≤x≤3π/2 and cosy=3/5 with 0≤y≤π/2, find the exact value of cos⁡(x-y)

Answer 1

Answer:

• sin(x)=(-15)/17
• cos(x)=(-8)/17
• cos(y)=3/5
• sin(y)=4/5

$→\cos(x - y) = \cos(x)\cos(y) + \sin(x) \sin(y) \\ =(\frac{ - 8}{17}\times \frac{3}{5}) +(\frac{ - 15}{17} \times \frac{4}{5}) \\ = \frac{ - 24}{85} + \frac{ - 60}{85} \\ = \frac{ (- 24) + ( - 60)}{85} \\ = \boxed{ \frac{ - 84}{85} }✓$

(-84)/85 is the right answer.