thanks for the help :)

how will it be then if you have one like this 4 sin2(x) + 8 cos(x) = 7 ?

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- Dec 28th 2010, 01:17 PMpaulaaNeed help solving a trigonometric equation.
thanks for the help :)

how will it be then if you have one like this 4 sin2(x) + 8 cos(x) = 7 ? - Dec 28th 2010, 01:20 PMe^(i*pi)
If, as I assume, $\displaystyle \sin2(x) = \sin^2(x)$ then use the identity $\displaystyle \sin^2(x)+\cos^2(x) = 1$

Your equation will be $\displaystyle 4\cos^2(x)-8\cos(x)+3=0$ which does factorise but it's probably easier to use the formula to solve for cos(x). You can then find x. - Dec 28th 2010, 01:23 PMpickslides
Here's a kicker,

$\displaystyle 4 \sin 2x + 8 \cos x = 7$

$\displaystyle 4 \times 2 \sin x \cos x+ 8 \cos x = 7$

$\displaystyle 8 \sin x \cos x+ 8 \cos x = 7$

$\displaystyle 8 \cos x(\sin x+1) = 7$ - Jan 14th 2011, 11:46 AMharish21
- Jan 14th 2011, 12:01 PMpaulaa
i saw that now, but it will be the same answer ?

- Jan 14th 2011, 12:06 PMpaulaa
sorry i was wrong.

thank you : ) - Jan 14th 2011, 01:04 PMpaulaa
i didnīt understod everything so i did it this way

4sinēx + 8cosx = 7

sinē(x) + cosē(x) = 1 <=> sinē(x)=1-cosē(x)

replace sinē(x) with 1-cosē(x)

4(1-cosē(x)) + 8cos(x) - 7 = 0 <=> 4cosē(x) + 8cos(x) - 3 = 0

replace cos(x) with t

4tē + 8t - 3 = 0

tē + 2t - 3/4 = 0

(t+1)ē = 4/4 + 3/4 = 7/4

t1 = (7/4)^0.5 - 1

t2 = -(7/4)^0.5 - 1

x1 = cos^-1(((7/4)^0.5)-1)

but is this right to ?

**Moderator edit**: After deleting posts and moving things around, the ordering of how the posts should appear got messed up. For some of the responses in this thread to make sense, note that this post should come before post #4 (harish21's response). - Jan 14th 2011, 02:35 PMskeeter
- Jan 15th 2011, 10:44 AMpaulaa
the first equation:

i cant find the worong :/

sin(5x-((4x)/3) = 1/2

t=5x-((4x)/3)

sin(t)=1/2=sin(pi/6 +n*2pi)

5x - 4pi/3 = pi/6 + n*2pi

5x = 4pi/3 + pi/6 + n*2pi

5x = 9pi/6 + n*2pi

x = (9pi/6 + n*2pi)/5

x = 3pi/10 + n * 2pi/5

i think you will have 2 solutions will the other one be x = pi - 3pi/10 + n * 2pi/5

?