High yield5 mapped NDA questions
Build the idea
Trigonometry connects several NDA chapters: identities, triangles, heights and distances, inverse functions, calculus and coordinate geometry. Build every solution from the unit-circle signs, standard angles and three Pythagorean identities rather than memorising isolated tricks.
Concept
Trigonometric ratios relate the angles and sides of a right triangle. Identities (Pythagorean, sum/difference, multiple-angle) let you transform expressions and solve equations efficiently.
Knowing the standard-angle table and sign by quadrant is essential.
Key Points & Formulas
- sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
- sin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB.
- sin2θ = 2 sinθ cosθ; cos2θ = 2cos²θ − 1.
- Maximum of a sinθ + b cosθ is √(a²+b²); minimum is −√(a²+b²).
Worked Example
Q. If sinθ = 3/5 and θ is acute, find cosθ and tanθ.
cos²θ = 1 − sin²θ = 1 − 9/25 = 16/25 ⇒ cosθ = 4/5.
tanθ = sinθ/cosθ = (3/5)/(4/5) = 3/4.