Trigonometric Ratios & Identities

Trigonometry is based on right-angled triangles. The fundamental concepts Revolve around the relationship between the angles and the sides of a right triangle.

• Sine (sin $x$): Perpendicular (P) / Hypotenuse (H)
• Cosine (cos $x$): Base (B) / Hypotenuse (H)
• Tangent (tan $x$): Perpendicular (P) / Base (B)

You must memorize the standard values of angles to solve questions instantly without calculations.

Note: $\sin$ goes from $0 \rightarrow 1$ while $\cos$ goes from $1 \rightarrow 0$.

Determining the sign (+ or -) of a trigonometric function is based on which quadrant the angle falls into.

• 1st Quadrant (0° - 90°): All positive.
• 2nd Quadrant (90° - 180°): Sin and Cosec are positive.
• 3rd Quadrant (180° - 270°): Tan and Cot are positive.
• 4th Quadrant (270° - 360°): Cos and Sec are positive.

Mnemonic: Add Sugar To Coffee

These 3 identities are the backbone of advanced simplification questions:

Derivative Trick: If $\sec\theta + \tan\theta = k$, then $\sec\theta - \tan\theta = 1/k$. (Because $\sec^2 - \tan^2 = 1$)