SOLUTION: sin(135 degree)plus cos (150 degree)

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Question 170167: sin(135 degree)plus cos (150 degree)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Note: sin%2845%29=sqrt%282%29%2F2, sin%2860%29=sqrt%283%29%2F2, sin%2890%29=1, cos%2845%29=sqrt%282%29%2F2, cos%2860%29=1%2F2, and cos%2890%29=0


sin%28135%29=sin%2890%2B45%29=sin%2890%29cos%2845%29%2Bcos%2890%29sin%2845%29=%281%29%28sqrt%282%29%2F2%29%2B%280%29%2B%28sqrt%282%29%2F2%29=sqrt%282%29%2F2%2B0=sqrt%282%29%2F2


So sin%28135%29=sqrt%282%29%2F2



cos%28150%29=cos%2890%2B60%29=cos%2890%29cos%2860%29-sin%2890%29sin%2860%29=%280%29%281%2F2%29-%281%29%28sqrt%283%29%2F2%29=0-sqrt%283%29%2F2=-sqrt%283%29%2F2


So cos%28150%29=-sqrt%283%29%2F2



This means that


sin%28135%29%2Bcos%28150%29=sqrt%282%29%2F2%2B%28-sqrt%283%29%2F2%29=%28sqrt%282%29-sqrt%283%29%29%2F2



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Answer:


So sin%28135%29%2Bcos%28150%29=%28sqrt%282%29-sqrt%283%29%29%2F2