Trig Identities Game

Trig Identities Quiz/Game
This Trig Identity Matcher game will test your knowledge of how trigonometric functions relate to each other algebraically. Scroll down the page for a more detailed explanation.
 

 

How to Play

1. Analyze the Prompt:
   Look at the large white text in the center. Identify if it contains a fraction, a square, or a negative sign inside the parentheses.
   
   
2. Recall the Rule:
   Mentally scan your “identity bank.”
   
   
3. Select the Match:
   Click one of the four buttons.
   Green Flash: You matched correctly
   Red Flash: You missed it. The game will immediately highlight the correct answer in green so you can memorize it for the next round.
   
   
4. Scoring and Content
   The game tracks your progress in the top-left corner (Score: Correct / Total Attempts).
    
   

Here is a comprehensive list of the trigonometric identities used in this game, organized by their mathematical “family.” Understanding these groups makes it much easier to recognize them during the challenge.

1. Pythagorean Identities
   These are based on the Pythagorean theorem (a² + b² = c²) applied to the unit circle. They almost always involve squared terms and the number 1.
   Primary: \(\sin^2(\theta) + \cos^2(\theta) = 1\)
   Rearranged: \(1 - \cos^2(\theta) = \sin^2(\theta)\)
   Tangent Variant: \(1 + \tan^2(\theta) = \sec^2(\theta)\)
   Cotangent Variant: \(1 + \cot^2(\theta) = \csc^2(\theta)\)
   
   
2. Reciprocal Identities
   These define the “flip” relationships. If you see a function in the denominator of a fraction, it usually matches its reciprocal pair.
   Secant: \(\frac{1}{\cos(\theta)} = \sec(\theta)\)
   Cosecant: \(\frac{1}{\sin(\theta)} = \csc(\theta)\)
   Cotangent: \(\frac{1}{\tan(\theta)} = \cot(\theta)\)
   
   
3. Quotient Identities
   These identities express tangent and cotangent as a ratio of sine and cosine.
   Tangent: \(\frac{\sin(\theta)}{\cos(\theta)} = \tan(\theta)\)
   Cotangent: \(\frac{\cos(\theta)}{\sin(\theta)} = \cot(\theta)\)
   
   
4. Negative Angle (Even/Odd) Identities
   These tell you what happens when you plug a negative angle into the function.
   Sine (Odd): \(\sin(-\theta) = -\sin(\theta)\)
   Tangent (Odd): \(\tan(-\theta) = -\tan(\theta)\)
   Cosine (Even): \(\cos(-\theta) = \cos(\theta)\)
   
   
5. Cofunction Identities
   These describe the relationship between a function and its “co” counterpart (like sine and cosine) when the angles are complementary (sum to 90° or \(\frac{\pi}{2}\)).
   Sine to Cosine: \(\sin(\frac{\pi}{2} - \theta) = \cos(\theta)\)
   Cosine to Sine: \(\cos(\frac{\pi}{2} - \theta) = \sin(\theta)\)
    
   

This video gives a clear, step-by-step approach to learn trigonometric identities.

• Show Video

 

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