given sinx=-1/4 and 180

Question

given sinx=-1/4 and 180<x<270, determine the exact value of cos2x

amistre64 · Answer

lets find the cos of x..... think we can?

amistre64 · Answer

cos(2x) = cos(x)cos(x) - sin(x)sin(x)

amistre64 · Answer

sin^2(x) + cos^2(x) = 1

cos^2(x) = 1 - (-1/4)^2

cos^2(x) = 1  -1/16

cos^2(x) = 15/16

cos(x) = sqrt(15)/4

amistre64 · Answer

cos(2x) = sqrt(15)sqrt(15)       -1(-1)
                -------------  -  --------
                       4(4)                       4(4)

amistre64 · Answer

cos(2x) = 15 - 1
                 ------
                    16

cos(2x) = 14/16 = 7/8

anonymous · Answer

oh my gosh, that makes total sense now!  i just have trouble picking what identity or formula to use.

amistre64 · Answer

trig is 90% memorizing

anonymous · Answer

yeahh, tell me about it. but thank you!

amistre64 · Answer

the only time your gonna have to actually worry about this stuff is in calculus classes when you try to manipulate formula into derivatives and integrals.... other than that....pointless.  A calculator gives you all the answers

anonymous · Answer

ohh gotcha. but why do you use cos2x= cosxcosx - sinxsinx?  i thought that was a sum and difference formula? im just a little confused with that part.

amistre64 · Answer

since they want you to find cos(2x)  and give you sin(x)  its only natural :)

anonymous · Answer

oh, okay got it!