The CAST diagram - a quick explanation

This is a quick demonstration of how to use the CAST diagram to find all the potential solutions to a trigonometric equation. There is a video with a more complete explanation in the A Level playlist for pure maths.

[@eggmaster1233]

I have been struggeling with this topic but finally I have found someone who breaks it down in a quick and simple manner. Thanks!

[@MathsBoost]

Thanks for letting me know!

[@squishi3941]

Superb, Thank you. Short, snappy, and you get straight to the point, perfect. I'm 4 years late, and it's still great.

[@MathsBoost]

Thanks!

[@cluckoothechicken5721]

Thank you! This finally put and end to my misery !!!

[@MathsBoost]

Great to hear!

[@smurfart201]

Bro u taught me a 2 hour lesson in 4 minutes. HUGE KUDOS!!!

[@MathsBoost]

Great - thanks for letting me know!

[@Eyebroooo]

Thanks I almost forgot how to use this diagram.

[@tenboku3515]

hey what about if then angle is 0, 180, 270 or 360?

[@MathsBoost]

A great question. The method still works but most students would probably be happier with an explanation first. Sin (180). Draw in the arm of the angle. It will be drawn from the centre and out horizontally left. . Draw in the related acute angle - it is 0 degrees on the x axis. But is it in the 2nd or 3rd quadrant? Pick either one!!! If you choose it as 0 degrees in the 2nd quadrant then the sine function is positive here and you will draw in 0 degrees in the other positive quadrant - the first quadrant. The arm of the angle will be drawn from the center and horizontally to the right. You now have two angles 0 and 180. If you choose it as 0 degrees in the 3rd quadrant then the sine function is negative here and draw 0 degrees in the other negative quadrant - the 3rd quadrant. The arm of the angle will still be drawn from the center and horizontally to the right. You now have the same two angles 0 and 180. I might update the video to incorporate this as a visual explanation is always better and I'm not sure this conveys the idea. All the angles and trig functions will 'work out' like this.

[@mhnd-ig8tw]

Great video!

[@MathsBoost]

Thanks!

[@theamazingguy150]

Thanks very helpful

[@MathsBoost]

Glad it's helped out

[@patrickainsworth3710]

Thanks

[@frymeup9363]

ty

[@MathsBoost]

Thanks - always nice to hear a video's been useful

[@the_hasnat]

good.

[@samnewman4314]

how did you know which quadrant cos is negative?

[@MathsBoost]

The letters in C A S T represent the trig' ratio which is positive. For example in the quadrant with 'S' Sin is positive and consequently Cos and Tan are negative. In the quadrant with 'T' Tan is positive and consequently Sin and Cos are negative. in A all ratios are positive - none are negative.