How to solve cos7pi/6 in baby steps?

[meatandpotatoes22003]

Can someone break down in "baby steps" how to solve the following?:

cos7pi/6=?

thank you. :uhh:

 

[Gaz031]

Can someone break down in "baby steps" how to solve the following?:

cos7pi/6=?

thank you. :uhh:

You can either use the CAST quadrant diagram or the cos(A+B) formulae, but both rely on you knowing cos(pi/6)=(rt3)/2

 

[SteveRives]

Q. How many times does pi go into a circle?
A. Two times. And that is the same as going 360 degress.

Q. Then half a circle is has one pi?
A. Right.

Q. So pi is like 180 degrees?
A. Right, and Cos of 180 degress is Cos 6pi/6. And that is like having a trinangle that has no opposite edge. Such a triangle is not much of a triangle, O / H is zero.

Q. So what is Cos 6pi/6?
A. It is A/H where A and H are the same lenght, only we are going in a negative direction for A (relative to the X axis).

Q. That means Cos 6pi/6 is -1?
A. That's right.

Q. Okay, that takes care of Cos 6pi/6, what about Cos 7pi/6?
A. Well, that's like going 1/6th of pi (where pi is 180 degrees) farther than we already have. We've gone 6pi/6 to sweep half a circle, now we go a little more beyond that.

Q. So that would be 30 degrees more, right?
A. Right, becasue six times 30 is 180, and we want 1/6th more of that; so we go the extra 30 degrees to make 7/6th of pi.

Q. So we are talking about a triangle with a 30 degree angle?
A. That's right, and it is drawn along the negative x-axis below it.

Q. So how do I find Cos 30 degrees?
A. You can draw a 30 degree triangle with a protractor and measure the ratio of A/H.

Q. So will it be positive or negative?
A. Even though it is a 30 dgree triangle, it has been layed along the X axis on the negative side. So A will be negative in the A/H ratio.

 

[mathwonk]

look at a circle. and find 7pi/6. then ask what the coordinates of that point are.

 

[VietDao29]

Why don't you use:
$$\cos(\pi + \alpha) = -\cos{\alpha}$$
Viet Dao,