Tuesday

September 2, 2014

September 2, 2014

Posted by **sqleung** on Saturday, March 1, 2008 at 1:52am.

sin x - sin 3x + sin 5x = 0

-¦Ð ¡Ü x ¡Ü 0

------

Now, using my graphics calculator, I discovered that the following equation has 5 solutions. I have managed to come up with 3 of them but I'm having trouble finding the other 2. My 3 answers are:

0, -¦Ð/6, -5¦Ð/6

I need the answers to be EXACT like above so any help would be appreciated. Thankyou.

- Trig Equation -
**drwls**, Saturday, March 1, 2008 at 7:25amI answered this question two days ago. Once of the answers is of course x = 0. For the others, I substitued indentities for sin 3x and sin 5x in terms of sin x, and ended up with a factorable equation for sin x. This leads to exact equations for arcsin in terms of fractions.

I am not able to read your terms -¦Ð/6 and -5¦Ð/6

If I can find my original answer, I will post a link to it below

- Trig Equation -
**drwls**, Saturday, March 1, 2008 at 7:46amOK, I found my original answer at

http://www.jiskha.com/display.cgi?id=1204243109

and it has two mistakes, a missing exponent and an incorrect sign. I should have ended up with the equation

3sinx - 16 sin^3x + 16sin^5x = 0

which factors to

sinx (3 - 16sin^2x + 16sin^4x) = 0

sinx (4sin^2x-3)(4sin^2x -1) = 0

Thge roots, besides x=0, are:

sin^2x = 1/4

sin x = +/-sqrt(1/2)

and

sin^2 = (3/4)

sin x = +/-(sqrt3)/2

- Trig Equation -
- Trig Equation -
**drwls**, Saturday, March 1, 2008 at 10:31amAny positive or negative integral multiple of 30 degrees (x=pi/6), including 0 degrees, satisfies the equation.

- Trig Equation (correction) -
**drwls**, Saturday, March 1, 2008 at 11:25amAll +/- integral multiples of pi/6 EXCEPT multiples of pi/2 are solutions

- Trig Equation (correction) -

**Answer this Question**

**Related Questions**

Maths - Solve for x (exact solutions): sin x - sin 3x + sin 5x = 0 ¦Ð ¡Ü x...

math - Eliminate the parameter (What does that mean?) and write a rectangular ...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

MathsSs triG - Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-...

tigonometry - expres the following as sums and differences of sines or cosines ...

Calculus - I need to find the exact solutions on the interval [0,2pi) for: 2sin^...

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

trig - give the exact real number value without using a calculator sin[(cos^-1)(...

Math (Trig) - Solve the equation for exact values of x. sin(x) = 1-2(sin(x))^2

algebra - Can someone please help me do this problem? That would be great! ...