Red = Sine (y-axis) | Blue = Cosine (x-axis) | Purple = Tangent (sin/cos)
Pink = Cosecant (1/sin) | Light Blue = Secant (1/cos) | Light Purple = Cotangent (1/tan)
On the unit circle: x = cos ฮธ and y = sin ฮธ
The cheatsheet contains 45 identities. The mnemonic directly organizes 24 core identities: 16 in the top string and 8 in the product-to-sum and sum-to-product grid.
Read the top string as identity families:
Click or hover the compact sign/code key to reveal the product-to-sum and sum-to-product relationship. The four columns are:
Use the color-coded letters to track sine and cosine. Product-to-sum begins with ยฝ; sum-to-product keeps the factor 2 and places the angle combinations over 2. Hovering a code or sign highlights only the matching pieces in both formulas, so you can infer the connection instead of memorizing two unrelated lines.
Check identities to study. Selected items show details by default (click to collapse).
Presets: Use the dropdown to quickly load curated sets:
Toggle Quiz Mode from the cheatsheet page to hide each formula until you tap an identity to reveal it.
Desktop Controls:
Mobile: Tap any identity to reveal its formula.
๐ Interactive Unit Circle App - Visualize trig functions on the unit circle