SOLUTION: when sin x= -8/17 and x lies in Quadrant III and cos y= -4/5 and y lies in Quadrant II, what is cos(x-y) ?

Question 830487: when sin x= -8/17 and x lies in Quadrant III and cos y= -4/5 and y lies in Quadrant II, what is cos(x-y) ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
when sin x= -8/17 and x lies in Quadrant III where x < 0 and y < 0
Find cos(x)::::::
sin = y/r, so y = -8 , r = 17
Then x = -sqrt[17^2-8^2] = -sqrt[225) = -15
So cos = x/r = -15/17
============================================================
and cos y= -4/5 and y lies in Quadrant II
Find sin(y)::::::
y = sqrt[25-16] = 3
So sin = y/r = 3/5
==========================================================
What is cos(x-y) ?
------
Formula: cos(x-y) = cos(x)cos(y)+sin(x)sin(y)
-----
cos(x-y) = (-15/17)(-4/5) + (-8/17)(3/5)
= (0.7059)+(-0.2824) = 0.4235
========================
Cheers,
Stan H.

RELATED QUESTIONS
Given: A lies in Quadrant III and B lies in Quadrant II, m1212. Find the exact value... (answered by lwsshak3,solver91311)

Evaluate each expression under the given conditions. tan(x+y) given cos(x)=-(1/3) (answered by richard1234)

Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in... (answered by lwsshak3)

given sin(x)=5/13 and x is in quadrant II what is... (answered by stanbon)

find tan(x-y) if sin(x)=8/17 and cos(y)=3/5 and x and y are both in the first quadrant.... (answered by KMST)

Find cos (theta) and sin (theta) if the terminal side of (theta) lies along the line y =... (answered by robertb)

find the exact value of sin(2x) and cos(2x) and the quadrant in which 2x lies, given that (answered by Alan3354)

if sin theta = - 5/13 and theta lies in quadrant 4 what is the value of cos... (answered by josmiceli)

tan α = 12/5, α lies in quadrant III, and cos β = -20/29 , β lies in... (answered by tommyt3rd)