Monday

March 2, 2015

March 2, 2015

Posted by **Anonymous** on Wednesday, November 21, 2007 at 6:29pm.

3sinx = 2cos^{2}x

-----

I don't know how to solve this equation...this is what I have, but I don't know if I'm on the right track or not

3sinx = 1 - 2sin^{2}x

3sinx - 1 + 2sin^{2}x = 0

2sin^{2}x + 3sinx - 1 = 0

sinx(3 + 2sinx) = 1

...and if I am, what do I do next now?

-----

The answers are:

30 and 150 degrees

- Math - Solving Trig Equations -
**Michael**, Wednesday, November 21, 2007 at 6:35pm3sinx = 2cos^2(x)

I believe you've treated this as cos(2x) and expanded it as a double-angle identity. However, you can't do this because the cosine function is being squared. The 2 is not being multiplied by the x.

I'm working on it...

- Math - Solving Trig Equations -
**Michael**, Wednesday, November 21, 2007 at 6:43pmStart by recalling the most important identity. My math teacher calls this "the #1 Identity."

sin^2(x) + cos^2(x) = 1

We want to simplify our trig equation by writing everything in terms of sine. Let's solve the #1 Identity for cos^2(x) because we have that in our trig equation.

cos^2(x) = 1 - sin^2(x)

Plug that into the trig equation, and see what you can get from there. Let me know if you get stuck along the way.

- Math - Solving Trig Equations -
- Math - Solving Trig Equations -
**Anonymous**, Wednesday, November 21, 2007 at 6:49pmwow I forgot about that identity, thank you!

But, I'm still stuck...

I get

cos^2x + sin^2x = 1

I can't use any compound identities for this...I don't know how to isolate for either cos or sin...

- Math - Solving Trig Equations -
**Michael**, Wednesday, November 21, 2007 at 6:57pmThe only identity you need it the #1 Identity.

Plugging in 1 - sin^2(x) for cos^2(x), you should get...

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

Use the distributive property, collect everything on the left, and then factor.

- Math - Solving Trig Equations -
**Michael**, Wednesday, November 21, 2007 at 6:57pmThe only identity you need is the #1 Identity.

Plugging in 1 - sin^2(x) for cos^2(x), you should get...

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

Use the distributive property, collect everything on the left, and then factor.

- Math - Solving Trig Equations -
- Math - Solving Trig Equations -
**Anonymous**, Wednesday, November 21, 2007 at 7:09pmthanks, I solved it :)

- Math - Solving Trig Equations -
**Michael**, Wednesday, November 21, 2007 at 7:38pmGlad to be of service. :)

- Math - Solving Trig Equations -

**Answer this Question**

**Related Questions**

Math - Solving for Trig Equations - Solve the following equation for 0 less than...

Math - Solving Trig Equations - Solve each equation for o is less than and/or ...

Math - Solving Trig Equations - Solve each equation on the interval: 0 is less ...

Solving inequalities - I have to solve the following inequalities: x^2 + y^2 is ...

Precalculs - I have no idea how to do these type of problems. -------Problem...

trig - how do i get the degree for (tan+1)(tanx-2)=0 in the interval of 0 is ...

Trigonometry - Solve for the following equation to the nearest degree if needed ...

Math/Trig - Solve: sin2 x = cos2 x for 0 degrees is less than or equal to x is ...

Math/Trig - Solve: 2 sin x - 1 = 0 for 0 degrees is less than or equal to x is ...

trigonometry - solve the equation: 4 tan^2 x + 12 sec x +1 =0, for 0 degrees is ...