Posted by Help on Sunday, April 1, 2012 at 1:13am.
1st one:
2sin(2x) = cosx
4sinxcosx - cosx = 0
cosx(4sinx - 1) = 0
cosx = 0 or sinx = 1/4
for cosx = 0
x = 90° or 270° OR x = π/2 or 3π/2 radians
for sinx=1/4
x = appr 14.5° or 165.5° OR appr .253 or 2.89 radians
2nd:
cos^2(2x)–sin^2(2x)= (√3 / 2)
cos (4x) = √3/2 , using cos (2A) = cos^2 A - sin^2 A
I know cos 30° = cos 330° = √3/2
so 4x = 30° or 4x = 330°
x = 7.5° or x = 82.5°
the period of cos 4x is 360/4 ° = 90°
so adding or subtracting multiples of 90 to any of the above solutions, will yield a new solution
e.g. 7.5 + 90 = 97.5°
97.5+90 = 187.5° etc
check for x = 187.5°
LS = cos^2 375° - sin^2 375°
= .9330... - .0669...
= .866025...
RS = √3/2 = .866025...
= LS
(set your calculator to Radians using the DRG key, and get the equivalent answers in radians)
Related Questions
TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
Math - Solving for Trig Equations - Solve the following equation for 0 less than...
Math - Prove each identity: a) 1-cos^2x=tan^2xcos^2x b) cos^2x + 2sin^2x-1 = sin...
Math - Solving Trig Equations - Solve each equation for o is less than and/or ...
Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...
trigonometry (please double check this) - Solve the following trig equations. ...
trig - For each expression in column I, choose the expression from column II to ...
Math (Trig) - sorry, another I can't figure out Show that (1-cot^2x)/(tan^2x...
trig - The expression 4 sin x cos x is equivalent to which of the following? (...
pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...
For Further Reading
