Trigonometry for SSC CGL Cheat Sheet

Key Definitions

• Trigonometry: Study of relationships between angles and sides in triangles.

• Angle: Measured in degrees (°) or radians (rad).

• Sine (sin): Ratio of opposite side to hypotenuse.

• Cosine (cos): Ratio of adjacent side to hypotenuse.

• Tangent (tan): Ratio of opposite side to adjacent side.

Important Concepts

Trigonometric Ratios

• Basic ratios: sin θ, cos θ, tan θ

• Reciprocal ratios: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ

Pythagorean Identity

• sin² θ + cos² θ = 1 ✅

Angle Sum and Difference

• sin(a ± b) = sin a cos b ± cos a sin b

• cos(a ± b) = cos a cos b ∓ sin a sin b

• tan(a ± b) = (tan a ± tan b) / (1 ∓ tan a tan b)

Key Formulas

sin² θ + cos² θ = 1 ✅
tan θ = sin θ / cos θ ✅
sin 30° = 1/2 ✅
sin 45° = √2/2 ✅
sin 60° = √3/2 ✅
cos 30° = √3/2 ✅
cos 45° = √2/2 ✅
cos 60° = 1/2 ✅
tan 30° = 1/√3 ✅
tan 45° = 1 ✅
tan 60° = √3 ✅

Common Mistakes to Avoid

Common Mistake: Confusing sin, cos, and tan values for standard angles.

Memory Tricks

Tip: "SOH-CAH-TOA" —

• Sine = Opposite / Hypotenuse

• Cosine = Adjacent / Hypotenuse

• Tangent = Opposite / Adjacent

Key Diagrams

        |\
      h | \
        |  \ o
        |   \
        |____\
          a

• h: Hypotenuse

• o: Opposite side

• a: Adjacent side

Tip: Always label sides in right triangles to avoid confusion.