Worked example 1
Question: If tanθ=3/4 for an acute θ, find sinθ and cosθ.
Solution: Take opposite=3k, adjacent=4k. Hypotenuse=5k by Pythagoras. Therefore sinθ=3/5 and cosθ=4/5.
What this chapter covers
Define the six trigonometric ratios for an acute angle, use standard angle values, and connect ratios with simple identities.
Ratios in a right triangle
Relative to angle θ: sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. Their reciprocals are cosecant, secant and cotangent. Ratios depend on the angle, not the triangle’s size, because right triangles with the same acute angle are similar.
Standard angles and identities
Memorise sin, cos and tan values for 0°, 30°, 45°, 60° and 90° where defined. Use complementary ratios and reciprocal relationships to simplify expressions.
Key formulae: tanθ=sinθ/cosθ; sin²θ+cos²θ=1; 1+tan²θ=sec²θ; 1+cot²θ=cosec²θ.
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: Evaluate 2sin30°+cos60°−tan45°.
Solution: 2(1/2)+(1/2)−1=1/2.
Practical activity / investigation
Make a 30°–60°–90° triangle from paper, measure its sides, and calculate sin, cos and tan for 30° and 60°. Compare your ratios with the standard table; explain small differences as measurement error.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: If sinθ=5/13 for acute θ, find cosθ.
Adjacent=√(13²−5²)=12, so cosθ=12/13.
Practice 2: Evaluate sin²45°+cos²45°.
By the identity the value is 1.
Practice 3: Write tan60° and cos30°.
tan60°=√3 and cos30°=√3/2.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.