Solving Cosine of 330 Degrees: Conjugate Method vs. Alternative Method Explained

[Hammad Shahid]

Homework Statement

Cos(330 degrees)
*No calculator

Homework Equations

(a^2)+(b^2)=(c^2)
Cos=(delta x / hypotenuse)

The Attempt at a Solution

Hi guys, so today at school, the teacher was doing a problem which stated to solve the cosine of 330 degrees. The teacher used the conjugate angle method to get the answer 0.866.
However, I do not see what is wrong with my method (link to image will be below), because when I do it, I get -0.5. Please help, this has been frustrating me- I do not get why the conjugate method works, but not the one I used.
How I did it: https://imgur.com/a/Vp3ne

 

[Orodruin]

delta x / hypotenuse

You are taking $\delta y$ divided by the hypothenuse ... You are computing the sine, not the cosine.

 

[Hammad Shahid]

You are taking $\delta y$ divided by the hypothenuse ... You are computing the sine, not the cosine.

Sorry, I meant in relation to the angle, like such: https://imgur.com/a/hdKyE

IDK, it’s something my teacher showed me last year, like tangent = (y/x), or opposite/adjacent.

 

[Orodruin]

You really should not be using those terms for angles larger than 90 degrees, it will most likely just confuse you.

What you are computing is the sine, no matter how you frame it. The easiest way to remember things is to look at the unit circle with the angle ccw from the x axis. The x value is the cosine and the y value the sine.

 

[Hammad Shahid]

You really should not be using those terms for angles larger than 90 degrees, it will most likely just confuse you.

What you are computing is the sine, no matter how you frame it. The easiest way to remember things is to look at the unit circle with the angle ccw from the x axis. The x value is the cosine and the y value the sine.

Hmm, okay. However, wouldn’t that then technically be the same as cosine of -30 degrees?
But over here, 330-270=60 degrees.
So the only logical thing I can think of is that I have to view the angles in relation from the x-axis, Am I correct in saying that?

 

[SammyS]

But over here, 330-270=60 degrees.
So the only logical thing I can think of is that I have to view the angles in relation from the x-axis, Am I correct in saying that?

Yes. View it in relation to the x-axis.

 

[Hammad Shahid]

Ok. Now that I think about it, it makes a lot of sense.
Thank you both of you guys.

 

[Orodruin]

Hmm, okay. However, wouldn’t that then technically be the same as cosine of -30 degrees?

Yes. Both sine and cosine are periodic with a period of 360 degrees.