Cosine funtion expression

Problem: 6cosx+2=-1

Directions: solve for x. a)Write an expression that identifies all possible real answers (n= any integer) b) Give an answer that is within the principal values.

We went over this today in class, the answers were: a) 120+360n and 240+360n b) x=120

I'm confused about how to arrive at this answer. Also, is it possible to solve this without a graphing calculator?

Re: Cosine funtion expression

Hey Xelaza.

Hint: Re-arrange to get cos(x) = blah and tell us what principal angle corresponds to this particular x.

Re: Cosine funtion expression

6cosx+2=-1

-2 -2

6cosx=-3

/6 /6

cosx=-1/2

inverse

x=cos-1(-1/2)

Re: Cosine funtion expression

So what angle does this correspond to in the principal branch (Hint: Consider 30 and 60 degrees).

Re: Cosine funtion expression

Re: Cosine funtion expression

Then you need to learn more trig! There are a few values of trig functions that can be derived easily.

Note Chiro's "Hint: Consider 30 and 60 degrees". Draw an equilateral triangle with sides of length 2. What are its angles? Draw a perpendicular from one vertex to the opposite side. That also bisects both angle and side length. That gives you two right triangles. What are the angles in those right triangles? What is the length of the hypotenuse? What are the lengths of the legs? (One is easy, the other requires the Pythagorean theorem.) Now that you know the side lengths what are the sine and cosine of the angles?

Another "easy" angle is 45 degrees. Draw a right triangle with legs of length 1. What is the length of the hypotenuse? What are the angles?