Trig Special Angles Game

Trig Special Angles Quiz/Game
The trigonometric ratios for special angles like 0°, 30°, 45°, 60°, and 90° are fixed values. These exact values are derived from the properties of special right triangles, specifically the 45-45-90 and 30-60-90 triangles. Scroll down the page for a more detailed explanation.
 
This game that is designed to help you learn the trigonometric ratios for special angles (0°, 30°, 45°, 60°, and 90°) or their radian equivalents (0, \(\frac{\pi}{6}\), \(\frac{\pi}{4}\), \(\frac{\pi}{3}\), \(\frac{\pi}{2}\)). It will present you with a trig problem (like sin(30°)), and you will choose the correct simplified answer from a list of options. If you make a mistake, the game will show you the correct answer.
 

 

How to Play the Trig Special Angles Game
The game will challenge you to find the trigonometric ratios for special angles.
Here’s how to play:

1. Set Your Mode
   When you launch the game, you first choose your Angle Format.
   Degrees: Best for beginners. You’ll see numbers like 0°, 30°, 45°, 60°, and 90°.
   Radians: Best for advanced students. You’ll see fractions like 0, \(\frac{\pi}{6}\), \(\frac{\pi}{4}\), \(\frac{\pi}{3}\), \(\frac{\pi}{2}\).
   
   
2. Identify the Problem
   At the center of the screen, you will see a trigonometric function and an angle, for example:
   sin (30°) or \(\sin\left(\frac{\pi}{6}\right)\)
   Your goal is to find the exact value of that ratio.
   
3. Select and Check
   Pick an Answer: Click one of the four buttons in the grid.
   Feedback:
   If you are Correct, the button turns Green and your score increases.
   If you are Wrong, the button turns Red, and the game will highlight the Correct answer in green so you can learn from the mistake.
   Next: Click “Next Question” to generate a new random problem.
    
   

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 following table:

 
Sine:
Think of the numerator as 0, √1, √2, √3
The denominator is always 2.
Simplified: 0, \(\frac{1}{2}, \frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}\)
Cosine:
Think of the numerator as √3, √2, √1, 0
The denominator is always 2.
Simplified: \(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2}, \frac{1}{2}\), 0
Tangent:
Use the relationship
tan(θ)=sin(θ)/cos(θ)
Simplified: 0, \(\frac{\sqrt{3}}{3}\), 1, √3, Undefined
 

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
 

Use “Hand Trick”
The following video will show you how to find the trig ratios using the hand trick.

• Show video

 

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