Another Maths Question

[Huggybear16]

I posted here a few months ago with another maths question and got a lot of help, so was hoping you could explain how to arrive at the solution for this problem.

Q. What is the exact value of cos 210°?

I know the exact values of sin/cos/tan at 30°, 45°, 60° but can't work out how to get cos 210°

The answer is -(sqrt3)/2

My theory - because it is 30° along from 180° and therefore the same value as 30° along from 0 (+ve (sqrt3)/2) but at the other side of the x-axis (-ve y instead of +ve)? (Couldn't think of a clearer way to describe what I was thinking, hopefully you know what I'm trying to say)

Is this correct? How would you explain this? Are there any resources that you could recommend for me to study more on this, preferably with lots of worked (explained) examples.

Look up "CAST diagrams" 😊

By far the easiest way to understand this (and your thinking is on the right track) is to plot the graph. If you go from 1 to -1 on the y-axis, 0-360 on the x-axis, you can see the pattern. Plot it on Geogebra or similar and you can see how the patterns emerge.

I thought I knew about CAST diagrams - but clearly I dont. I got as far as "3rd quadrant, negative, 180° plus.....oh, I dont know what I'm doing here" - the CAST I remember from back in the day was far simpler. I think looking into this will be a good place for me to start.

I've just googled Geogebra as I haven't heard of this before. It looks great. I'm going to have a look at it tonight and have a play around with it.

What you said about sketching the diagrams (-1 to 1, 0 to 360) is what I have been doing, and was how I came up with the answer. I need more practice with this.

Thank you both.

This link for cosine and sine graphs from the unit circle is good for seeing what’s going on
www.geogebra.org/m/G9mjcC7D

If you think about a circle, centred at O with radius 1, and then trace around the points on the circumference of the circle. Then cos(theta) is the x coordinate and sin(theta) is the y coordinate of the points (theta is the angle from the positive x-axis going anticlockwise)
Then you can think of CAST diagrams as being a summary of this without the circle drawn.