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Trigonometry looks like a new subject with new symbols. It is not. It is a bookkeeping system for one shape — the right-angled triangle — and once you accept that, every question in the chapter becomes the same question wearing a different coat.
Take any right triangle and fix one acute angle θ. The side facing θ is the perpendicular, the side lying beside it is the base, and the longest side, opposite the right angle, is the hypotenuse. The six trigonometric ratios are nothing more than the six ways of dividing one of those three sides by another.
That is the entire foundation. The identities are Pythagoras rewritten. Heights and distances are word problems that draw this same triangle for you. The standard-angle values are one small table you memorise once.
SSC CGL, CHSL and MTS, RRB NTPC and Group D, and BPSC TRE-4 secondary mathematics all draw from this single chapter — and they draw the same handful of patterns year after year.
1. The value of sin 30° + cos 60° is:
2. If tan θ = 3/4, then the value of sin θ is:
3. The value of sin²25° + sin²65° is:
4. The value of (1 + tan²θ) × cos²θ is:
5. A tower 30 m high casts a shadow 30√3 m long on the ground. The angle of elevation of the sun is:
6. The angle of elevation of the top of a vertical pole from a point on the ground is 45°. If the pole is 18 m high, the distance of the point from the foot of the pole is:
7. The value of cos²30° − sin²30° is:
8. From the top of a 60 m high building, the angle of depression of a car standing on the ground is 60°. The distance of the car from the foot of the building is: