Thread: Trig Equation

How do I solve 6cos(3x) = 3 without using the unit circle?

Are there any restrictions on x? Usually we solve with the restriction . If that's the case, then we'll need to expand on pickslides' work a bit. If we have the restriction , then it follows that .

Originally Posted by pickslides

Between 0 and 2 pi we also have 5pi/3 as a possible answer:



For each answer, we need to find coterminal angles to it that is in , so we add 2pi and 4pi to each:








Now take each equation and divide both sides by 3 to solve for x. So we'll get


These are all possible values of x that is in .


01

Yeongil is correct to show 6 solutions, although given the following

Originally Posted by magentarita

without using the unit circle?

I would only give the 1 solution using the triangle made with angles and ignoring the unit circle.

Originally Posted by pickslides

Yeongil is correct to show 6 solutions, although given the following



I would only give the 1 solution using the triangle made with angles and ignoring the unit circle.

I need more than one or two answers.

Originally Posted by yeongil

Are there any restrictions on x? Usually we solve with the restriction . If that's the case, then we'll need to expand on pickslides' work a bit. If we have the restriction , then it follows that .



Between 0 and 2 pi we also have 5pi/3 as a possible answer:



For each answer, we need to find coterminal angles to it that is in , so we add 2pi and 4pi to each:








Now take each equation and divide both sides by 3 to solve for x. So we'll get


These are all possible values of x that is in .


01

This is exactly what I needed.

Hello: Here are the details for the solution :

The general solution is :

I'have :
but :
Calculate :
Case 1 :
but :
¨:

Case 2 :

We find :
¨
:

Thank you for all

Originally Posted by dhiab

Hello: Here are the details for the solution :

The general solution is :

I'have :
but :
Calculate :
Case 1 :
but :
¨:

Case 2 :

We find :
¨
:

Thank you for all

A very detailed reply!