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Trig. Equations Examples using CAST Diagrams

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Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths.

What is the CAST diagram?
The Cast diagram helps us to remember the signs of the trigonometric functions in each of the quadrants.
The CAST diagram is also called the Quadrant Rule or the ASTC diagram.

In the first quadrant, the values are all positive.
In the second quadrant, only the values for sin are positive.
In the third quadrant, only the values for tan are positive.
In the fourth quadrant, only the values for cos are positive.

Note that the mnemonic CAST goes anticlockwise starting from the 4th quadrant.

The following diagram shows how the CAST diagram or Quadrant rule can be used. Scroll down the page for more examples and solutions.
The cast diagram

Quadrant Rule or CAST diagram Using the Quadrant Rule to solve trig. equations



Quadrant Rule for solving trig equations with different ranges
Core (2) Graphs of Trigonometric Functions (4) - CAST Diagram or Unit Circle


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