Tuesday, February 26, 2008

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

2 comments:

NJTechTeacher said...

I wish I had someone help me with such thoughtful comments when I was back in high school. Sometimes it helps to see a problem in different ways. It was nice to see you give two methods to solve the problem. Unfortunately, I simply remember the sin(30)=1/2 cos(60)=1/2, so I couldn't comment on your solutions. I'm sure it helps clarify your thinking as you explain problems like these to other people. Nice job.

m@rk said...

njtechteacher,

Thank you for your positive feedback on my work.I really appreciate it. If i have some time I would definitely enjoy mentoring one of your class blogs.

Explaining my work to other people definitely helps clarify my thinking.Teaching to other people helps me apply what i learned before and helps me remember the concepts.

I remember that my teacher told me this, "You can't really say that you've learned something unless you've taught it to someone", so despite my busy schedule i still take a little of time to help other people.

-m@rk