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°). 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.
 

Special Angle Trig Ratios

Select the correct simplified value for each trig function.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Check Next

Back to Menu

 

How to Play the Trig Special Angles Game
The game will challenge you to find the trigonometric ratios for special angles (0°, 30°, 45°, 60°, and 90°).
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given a trigonometric problem.
   
3. Enter Your Answer: Choose the correct simplified answer from a list of options.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to remember the Trig Ratios?
There are three main methods to help you memorize the special trig ratios:

1. 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, 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
   
    
   

2. 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
    
   

3. 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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