Trigonometric Equations

While I was checking the blog for more questions to answer, I stumbled upon one of my classmates questions. This question is about trigonometric equations, so here was my response:

Benofschool,

Good job for trying to look for the answers. Your hard work only shows how dedicated you are to this class and how much effort you give into it.
Unfortunately, i don't think the answers are right.

Let's examine the first question first.

cos(2x)=1/2

Think of this as your regular algebra question. You can see that the only thing that is in your way is the cosine, so what you have to do is use arccos on both side to get rid of the cosine. That will leave you with this:

2x= 1.0472

Then with some more algebra you will get:

x= 0.5236 + kpi
AND the other other angle at quadrant 4 which is 2.6180 +kpi


Another way to solve this is to use the exact values of the unit circle.

cos2x= 1/2

We know that the cosine of 1/2 is pi/3, so that will leave you with this:

2x=pi/3

Now, again solving for x with some algebra we will get this:

x=pi/6+ kpi
AND
the other angle at quadrant 4 which is 5pi/6 +kpi

Im gonna let you finish up the next question. Hopefully that helps you in some way.

-m@rk