How do you find the exact value of #cos(u-v)# given that #sinu=-7/25# and #cosv=-4/5#?

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Answer 1 · 2017-12-02T14:09:23

The answer is #=-3/5#

We need

#cos^2x+sin^2x=1#

By definition,

#cos(u-v)=cosucosv-sinusinv#

#sinu=-7/25#, the angle is in the #4th# quadrant

#cosu=sqrt(1-sin^2u)=sqrt(1-(-7/25)^2)=(24/25)#

#cosv=-4/5#

The angle is in the #2nd# quadrant

#sinv=sqrt(1-cos^2v)=sqrt(1-(-4/5)^2)=(3/5)#

Therefore,

#cos(u-v)=(24/25)xx(-4/5)-(-7/25)xx(3/5)#

#=-96/125+21/125#

#=-75/125#

#=-3/5#