This is a quick resource that I made for my AS level maths students this week. It demonstrates how we can use identities to simplify and then solve a trig equation. You will always need to consider multiple solutions at A level. One option for this is to jot down a quick sketch graph of sin / cos / tan, or efficiently use a Graphical Calculator. However, the most fundamental and efficient way of finding multiple solutions from a trig equation is to sketch the simple CAST diagram.
Firstly, use your calculator to find an acute angle. Then draw arms into the relevant quadrants, according to whether your problem involves positive or negative values of sin, cos or tan. Visualise your final answers and write them down. So in this problem we need sin to be negative, ie 3rd and 4th quadrants, and the answers are 210 & 330 degrees.
Remember that in pure maths positive angles are swept out anti-clockwise from zero, whilst negative angles if required are swept out in the clockwise direction. The beauty and simplicity of the CAST approach, is that if the question had asked for answers in the range -180 to +180, then the diagram is the same but we visualise angles of -30 and -150 degrees.
AS/A level maths made easy! Any questions about this skill, then please message us in our website chat.
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