Question

cos(50) = t; determine cos(25) in terms of t

Answer 1

Hi , Welcome to OpenStudy :)
Do you know the standard formula for cos 2x ? in terms of cos x

Answer 2

thank you. I know the double angle formula for cos2x

Answer 3

good, so what is it ?

Answer 4

cos^2x -sin^2x

Answer 5

do you know any other form , which has only cos term ?

Answer 6

i know 2cos^2x-1

Answer 7

yes, thats what i was asking :)
so,
\(\cos 2x = 2\cos^2x-1\)
can you isolate cos x from that ?

Answer 8

oh sorry :) wouldnt cosx = square root( (1+ cos2x)/2) ?

Answer 9

correct ! good :)
so, in cosx = square root( (1+ cos2x)/2
just put x= 25
what u get ?

Answer 10

oh my goodness, i was so silly not to see that! you get square root((1+t)/2). Thank you so much for the help :) i really appreciate it!

Answer 11

your welcome ^_^