For A level students who want to work more efficiently in trigonometry, this is another quick dynamic that I created in DESMOS. It illustrates where sine, cosine, tangent take positive and negative values. In advanced level trig we consider positive angles to be swept out anti-clockwise from the x-axis. This is sometimes referred to as a quadrant diagram, or simply the CAST diagram.
Angles between 0 and 90 degrees are said to be in the 1st quadrant, angles from 90 to 180 are in the 2nd quadrant and so on.
The value of sin, cos, tan for any angle is the value of sin, cos, tan of the acute angle made with the x-axis along with the appropriate sign (+ - ). For example sin(120°) = sin(60°) whereas cos(120°) = -cos(60°) and tan(120°) = -tan(60°).
Using this dynamic allows to us solve equations to find multiple solutions for angles, without the need to sketch any of the trig graphs.
The simplicity and beauty of this diagram also allows you to give answers where required as negative angles. There is no additional process needed. You read off answers by visualising negative angles being swept out clockwise from the x axis. So 4th quadrant represents 0° to -90°, 3rd quadrant is -90° to -180° and so on.
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