factor the expression 3cos^2x+8cosx-3

Question

danjs · Answer

$$3\cos^2(x) + 8\cos(x) -3$$

Let :  cos(x) = u
$$3u^2 +8u - 3$$

danjs · Answer

can you factor that last expression?

anonymous · Answer

a little

anonymous · Answer

ik what to do

danjs · Answer

$$(3u \pm a)(u \pm b)$$

need to figure a and b

anonymous · Answer

ok

danjs · Answer

the factors of 3, are only 1 and 3

a and b will be 1 and 3, or 3 and 1

anonymous · Answer

oh and then you substitute the cis back in

anonymous · Answer

cos

danjs · Answer

yeah , after you factor in terms of u, sub back in u = cos(x)

anonymous · Answer

so (3cosx-1)(cosx+3)

danjs · Answer

$$(3u -1)(u + 3)$$

u = cos(x)
$$3\cos^2(x) + 8\cos(x) - 3~~=~~(3\cos(x) - 1)*(\cos(x) +3)$$

danjs · Answer

yep

anonymous · Answer

thanx and do you think you can help me with one more problem

danjs · Answer

sure

anonymous · Answer

determine the value of B in the equation 3+cos2B=-2sin^2B+7B

danjs · Answer

$$3 + \cos(2B) = -2\sin^2(B) + 7B$$

danjs · Answer

is that right

anonymous · Answer

yea and the B is suppose to be beta

danjs · Answer

+7 times beta at the end righ

anonymous · Answer

yea

danjs · Answer

do you remember the identity
$$\cos(2\beta ) = 1-2\sin^2(\beta)$$

anonymous · Answer

yea from the trig identities

danjs · Answer

$$3+[1-2\sin^2(\beta)] = -2\sin^2(\beta)+7*\beta$$

danjs · Answer

both sides now have -2sin^2(Beta)   and cancels out leaving just

3 + 1 = 7B

4 = 7B

B = 4/7

anonymous · Answer

wait how did the two -2sin^2 beta cancel

danjs · Answer

$$4-2\sin^2(\beta) = -2\sin^2(\beta)+7\beta $$

add$$+2\sin^2(\beta)$$to both sides

anonymous · Answer

oh ok

anonymous · Answer

how do ik when i need to use trig functions identities