Solve Trig Equation #2 on 0<=theta<=2pi

[Draggu]

Homework Statement

Solve for x on the interval 0<= theta <= 2pi. Give exact solutions if possible. Otherwise round to the nearest hundredth of a radian.

Homework Equations

tan^2x-4tanx = 0

The Attempt at a Solution

Tried factoring it to (tanx-4)(tanx) = 0

tanx=4 or 0 I guess? Not sure where to go from there

or instead of factoring I could immediately make it sin/cos, which gives

(sin^2x - 4sincos) / (cos^2x) = 0

 

[gabbagabbahey]

I would plot a graph of tan(x) for x \in [0,\pi]...at what points does tanx=4?...At what points does tanx=0?...Those will be your solutions.

 

[Дьявол]

"Tried factoring it to (tanx-4)(tanx) = 0"

@Draggu now it is good. So as you said there are two solutions: tanx=4 and tanx=0.

The solutions for x are:

x₁=[arctan(4)+kπ]

x₂=[arctan(0)+kπ]

Regards.

 

[Draggu]

"Tried factoring it to (tanx-4)(tanx) = 0"

@Draggu now it is good. So as you said there are two solutions: tanx=4 and tanx=0.

The solutions for x are:

x₁=[arctan(4)+kπ]

x₂=[arctan(0)+kπ]

Regards.

We have not learned that yet in class... so doing that wouldn't work. :p

 

[Draggu]

I would plot a graph of tan(x) for x \in [0,\pi]...at what points does tanx=4?...At what points does tanx=0?...Those will be your solutions.

There is no exact radian measure/degree where tanx=4
Tanx=4 approx at 76degrees. God I'm lost.

 

[Draggu]

Well I got: (19pi/45), (64pi/45), pi, 2pi as the answers

 

[Дьявол]

We have not learned that yet in class... so doing that wouldn't work. :p

You know how to draw graphic of tan function, and do not know how to find arctan(x)?

That's strange.

Anyway, you got the solutions correctly, since the task is to find the solutions in the interval [0,2п]. In the future, you will learn about periods.So if you want to be more correctly you should write 19п/45 + kп and п + kп, where k Є Z

 

[Chaos2009]

Well, for tan(x) = 0, you don't need to know tan(x). tan(x) = \frac{sin(x)}{cos(x)} so tan(x) = 0 when sin(x) = 0.