Question #46c50

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Answer 1 · 2018-01-05T08:19:37

#-cos^3(x)#

Since #630^circ > 360^circ# we can subtract #360^circ# for a more convenient coterminal angle: #630^circ - 360^circ=270^circ#

#sin^3(670^circ -x) = sin^3(270^circ -x)#

We can use the difference formula for sine on #sin(270^circ-x)#. The formula is:

#sin(a-b)=sin(a)cos(b)-cos(a)sin(b)#

So:

#sin(270^circ-x)=sin(270^circ)cos(x)-cos(270^circ)sin(x)#

Now remember that #cos(270^circ) = 0# and #sin(270^circ) = -1# so we can simplify the expression above:

#sin(270^circ)cos(x)-cos(270^circ)sin(x) = (-1)cos(x)-(0)sin(x)#

#=-cos(x)#

From this we have:

#sin^3(270^circ -x) = (sin(270^circ -x))^3=(-cos(x))^3#

#=(-1)^3cos^3(x) = -cos^3(x)#, which I think is as good as we're going to get.