Quandaries and Queries


My name is Lance, I am in 11th grade and taking precalulus.

My question is:

FIND ALL SOLUTIONS cosx=1-sin(x/2) if x[0,2pi)


Given cscx=-5/4 and cot>0, find csc(x/2) and cot(x/2)



Hi Lance,

For the first problem I would let y = x/2 and rewrite the expression as

cos(2y) = 1 - sin(y) But cos(2y) = 1 - 2 sin2(y) and hence you have 1 - 2 sin2(y) = 1 - sin(y) and hence 2 sin2(y) - sin(y) = sin(y) [2 sin(y) - 1] = 0 Solve for y then use the fact that x = 2y to find x. Make sure x is in [0,2pi).

I would use the same technique for the second problem, but first write the cosecant and cotangent in terms of sine and cosine.


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