Question

find the value of tan (a-b) if cos a=4/5 on the interval (270, 360) and sin b=-5/13 on the interval (270, 360)

Answer 1

We can find a and b using inverse trig functions,

$\cos(a)=\frac{4}{5}\implies a=\arccos\Big(\frac{4}{5}\Big)\approx36.87 \\\sin(b)=-\frac{5}{13}\implies b=\arcsin\Big(-\frac{5}{13}\Big)\approx-22.62$

$\tan(36.87-(-22.62))\approx1.7$

Hope this helps.