Trig. Equations Examples using CAST Diagrams

These lessons, with videos, examples and step-by-step solutions help A Level Maths students learn to solve trigonometric problems.

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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

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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