Saturday

April 19, 2014

April 19, 2014

Posted by **justy** on Monday, May 14, 2007 at 9:53pm.

solve the equation to the nearest tenth, where 0 degrees < or equal to x which is < 360 degrees.

8cos^2 3x-17cos3x+3=0

this doesnt factor, when i used the quadratic formula i got -17 plus or minus the square root of 193 over 2?? is that right?

Let the variable be u = cos 3x

8 u^2 -17 u +3 = 0

Use the quadratic equation to get the two "cos 3x" roots. Then use trig to get 3x

not quite

your solution would be

cos 3x = (17 ± sqrt(193))/16

cos 3x = 1.93.. or cos 3x = .194222

but the cosine of any angle lies between -1 and +1 so

cos 3x = .194222

then 3x = 78.8º or 3x = 281.2º

therefore x = 26.267º or x = 93.733º

Now lastly:

The period of cos 3x, which was the original trig function we were dealing with, is 360/3º or 120º

so other answers are obtained by adding 120 to each of my previous answers until we run over 360º

so x = 26.267, 93.733, 146.267,213.733, 266.267, 333.733

**Related Questions**

Algebra - 1)Find the exact solutions to 3x^2=5x-1 using the quadratic formula. ...

Algebra - I am a bit confused about conjugates in algebra. I am supposed to ...

Algebra (urgent!) - I am a bit confused about conjugates in algebra. I am ...

math - I am working on quadratic equations and I have worked a problem down to 3...

Algebra II - I am expected to use the quadratic equation for the following: x2...

college math - I'm hoping I did thesse right. Solve each quadratic equation. (I ...

Algebra2 - Find the polynomials roots to each of the following problems: #1) x^2...

Algebra - I am racking my brain trying to figure out how to work this: the ...

algebra - 1)Find the exact solutions to 3x^2=5x-1 using the quadratic formula. ...

math - 1.0 Four square root of seven open bracket two square root of three plus ...