# solutions of trigonometric equations..

QUESTION:the general solution of equation (√3 - 1)sin∅+(√3 + 1)c0s∅=2 is
1) ∅=2nπ+- (π/4)+(π/12)
2) ∅= nπ + (-1)^π (π/4)+(π/12)
3) ∅=2(n+1)π (π/4)+(π/12)

The answer is option 1 , i dont know why the last 2 options can be the solutions of the question as well.my teacher told me that to use 2nπ with sin and cos functions and nπ with tan functions.can someone please describe in detail about the periods used in solutions of trig.equations.THANKS

 ebaines Posts: 10,138, Reputation: 5589 Expert #2 Jul 24, 2012, 10:11 AM
Remember that the sine and cosine functions have periods of $2 \pi$, so that $\sin(\theta) = \sin (\theta \pm 2n \pi)$ and $\cos(\theta) = \cos(\theta \pm 2n \pi)$. Any solution to an equation involving sines and/or cosines will have general solutions with $\pm 2 n \pi$. Also recall that $\sin(\theta) = - \sin (\theta \pm \pi)$, and similarly $\cos(\theta) = - \cos (\theta \pm \pi )$, and hence the tangent function is periodic with period $\pi$, since the negative signs cancel out:

$
\tan \theta = \frac {\sin (\theta \pm n \pi)}{\cos (\theta \pm n \pi)} = \tan (\theta \pm n \pi)$
.

By the way, you wrote that the solution is

$\phi = 2 n \pi \pm \frac n 4 + \frac n {12}$

but I believe it's actually $\phi = \frac n 4 + \frac n {12} \pm 2 n \pi$
 subhan2010 Posts: 39, Reputation: 1 Junior Member #3 Jul 24, 2012, 09:32 PM
thank you....!

## Check out some similar questions!

To prove trigonometric equations [ 3 Answers ]

Could you please solve this problem? (cotA + CosecA - 1)/(cotA-cosecA+1) =(1+cosA)/sinA I have to prove that LHS = RHS.

Trigonometric equations [ 4 Answers ]

Prove (Sin5A - Sin4A)/(Cos4A + Cos5A) = Tan A/2

Trigonometric Equations [ 1 Answers ]

Determine the solutions for (1+secx) / (secx) = (sin^2x) / (1-cosx) in the interbal x E (-2pi, 2pi)

Trigonometric Equations [ 2 Answers ]

Hi all, I'm just new to this site. Looking a bit of help with my nightmare Analytical methods assignmnet on trigonometric equations :mad: Just need a bit of direction to get me on the right track with solving these for 0-360 degrees: 4-7sin(x)=0 15sin^2(A)+sin(A)-2=0 I also have to...

Solving trigonometric equations [ 1 Answers ]

Prove: Sin^3 X+cos^4 X=1 Here is what I have done so far: Prrof: sin^3x+cos^4x=1 sin^3x=1-cos^4x sin^3x=(1-cos^2x)(1+cos^2x) sin^3x=sin^2x(1+cos^2x) sin^3x-=0