Trig Ratios for multiples of 30, 45 and 60 degrees
Examples, solutions, and videos to help GCSE Maths students learn how to find the Trig Ratios for multiples of 30, 45 and 60 degrees.
The following diagram shows the trig ratios of special angles: 0°, 30°, 45°, 60°, and 90°. Scroll down the page for more examples and solutions on the trigonometric ratios.
Trigonometry Worksheets
Practice your trigonometry skills with the following worksheets.
How to remember the Trig Ratios?
There are three main methods to help you memorize the special trig ratios:
- Patterns in the table
Notice the following patterns in the above table.
Sine:
Think of the numerator as 0, √1, √2, √3
The denominator is always 2.
Simplified: 0, 1/2, √2/2, √3/2
Cosine:
Think of the numerator as √3, √2, √1, 0
The denominator is always 2.
Simplified: √3/2, √2/2, 1/2, 0
Tangent:
Use the relationship
tan(θ)=sin(θ)/cos(θ)
Simplified: 0, 1/√3, 1, √3, Undefined
Have a look at the following video.
- Use special triangles
Use the 45°-45°-90° Triangle and the 30°-60°-90° Triangle
Have a look at the following lesson for explanations on the special triangles.
Trig Special Triangles
The following video will show you how to calculate the exact values of sin, cos and tan of 45 degrees using the 45°-45°-90° Triangle.
The following video will show you how to calculate the exact values of sin, cos and tan of 30 and 60 degrees using the 30°-60°-90° Triangle.
- Use “Hand Trick”
The following video will show you how to find the trig ratios using the hand trick.
Trig. Ratios for positive multiples 30, 45 and 60 degrees
In this tutorial I show you how to calculate the exact values of sin, cos and tan for positive multiples of 30 and 60 degrees.
Trig. Ratios for negative multiples 30, 45 and 60 degrees
In this tutorial I show you how to calculate the exact values of sin, cos and tan for negative multiples of 30 and 60 degrees.
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