Help with a trig: sin6xcos5x-cos6xsin5x=sqrt3 * cosx

[oded244]

sin6xcos5x-cos6xsin5x=sqrt3 * cosx

 

[o_O]

For the left hand side of the equation, is there any trigonometric identity that you know that resembles this?

 

[oded244]

yes
i don't know what to do from sinx=sqrt3 cosx

 

[Mrspi]

yes
i don't know what to do from sinx=sqrt3 cosx

You may want to consider dividing both sides by cos x.....

sin x / cos x = sqrt(3)

Now....does that give you some ideas?

 

[oded244]

you sure i can do that?
the angle is not the same

 

[o_O]

What do you mean? There's only one angle: x.

 

[oded244]

you're right
i've copied the wrong one
i need help with this one:
sin4xcis3x+cos4xsin3x=cosx
sin7x=cosx

now, iv'e tried sin7x=sin(90-x)
but i don't know whats next

 

[o_O]

Perhaps this relation would help:

\(\displaystyle cosx = sin\left(x + \frac{\pi}{2} \right)\)

Hmm. Don't know why there's that arrow there.

 

[stapel]

sin6xcos5x-cos6xsin5x=sqrt3 * cosx

Were the instructions to "solve the equation"? If so, is there any particular interval, or are you supposed to find "all solutions"?

i need help with this one:
sin4xcis3x+cos4xsin3x=cosx
sin7x=cosx

Um... this is two equations, not one. Are they meant to be one exercise...? Either way, what are the instructions? And what is the meaning of "cis3x"?

Thank you!

Eliz.

 

[oded244]

sin4xcos3x+cos4xsin3x=cosx - all solutions
i've managed to get sin7x=cosx out of it, but i may be wrong

 

[o_O]

Did you learn anything about the graphs of sinx and cosx? And about radians?

Well if you're sticking with degrees: cosx = sin(x + 90°)

 

[oded244]

yep, im stuck in that equation
sin7x=sin(x + 90°)
i know its pretty basic but i would love to see the two solutions for it.

 

[o_O]

Have you learned anything about the unit circle yet?

One solution is to assume that the expressions inside the brackets are equal to each other. So if sinA = sinB, then A = B. Again, finding another solution or the general solution would be easier if you understood the unit circle but I'm not sure whether or not you've learned that yet. For me, I learned the unit circle first followed by trigonometric identities.

 

[oded244]

i've learned about the unit circle, still i see 2 answers to that equation when i only found one
x=11.25+45k
x=15+60k

 

[o_O]

Well following from what I was saying:
sin7x=sin(x + 90°)
7x = x + 90°
6x = 90°
x = 15°

Anyway, if you learned about the unit circle, then if you add 360° (or 2\(\displaystyle \pi\)) you will end up exactly at the same spot. If you add another 360°, you'll end up at the same spot again, giving you the same sine,cosine, tangent, etc. values. So what can you say about the general solution of x? Well you only need 2 but the concept is still the same

 

[Deleted member 4993]

cos(x) = sin[(4n+1)*(pi)/2 ± x]

 

[oded244]

got it
thanks guys