# Need help solving a trigonometric equation.

• Dec 28th 2010, 01:17 PM
paulaa
Need 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 PM
e^(i*pi)
If, as I assume, $\sin2(x) = \sin^2(x)$ then use the identity $\sin^2(x)+\cos^2(x) = 1$

Your equation will be $4\cos^2(x)-8\cos(x)+3=0$ 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 PM
pickslides
Here's a kicker,

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

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

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

$8 \cos x(\sin x+1) = 7$
• Jan 14th 2011, 11:46 AM
harish21
Quote:

Originally Posted by paulaa

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 = 0You missed the negative sign before 4cos^2x

$4(1-cosē(x)) + 8cos(x) - 7 = 0$

$-4 \cos^2(x)+8\cos(x)-3=0$

$4\cos^2(x)-8\cos(x)+3=0$

move on..
• Jan 14th 2011, 12:01 PM
paulaa
i saw that now, but it will be the same answer ?
• Jan 14th 2011, 12:06 PM
paulaa
sorry i was wrong.

thank you : )
• Jan 14th 2011, 01:04 PM
paulaa
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 PM
skeeter
Quote:

Originally Posted by paulaa
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

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

4cosē(x) - 8cos(x) + 3 = 0

[2cos(x) - 1][2cos(x) - 3] = 0

can you finish?
• Jan 15th 2011, 10:44 AM
paulaa
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

?