What is the general solution of sin θ = 0?

sin θ = 0 when θ = 0, π, 2π, −π, −2π, ... i.e., at all multiples of π. General solution: θ = nπ where n ∈ Z (any integer). Similarly, cos θ = 0 gives θ = (2n+1)π/2; tan θ = 0 gives θ = nπ.

How do you find sin 75° using compound angle formula?

sin 75° = sin(45° + 30°) = sin45°·cos30° + cos45°·sin30° = (1/√2)·(√3/2) + (1/√2)·(1/2) = √3/(2√2) + 1/(2√2) = (√3+1)/(2√2) = (√6+√2)/4.

What is the range of sin x and cos x?

Both sin x and cos x have a range of [−1, 1] — they can only take values between −1 and 1 inclusive. The domain is all real numbers R. Period = 2π. Maximum value 1 at x = π/2 (sin) and x = 0 (cos); minimum value −1 at x = 3π/2 (sin) and x = π (cos).

Trigonometric Ratios, Identities and Equations

Trigonometric Functions • Class 11 Mathematics • NCERT • CBSE

Trigonometric identities: sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ. Compound angles: sin(A+B) = sinAcosB + cosAsinB; cos(A+B) = cosAcosB − sinAsinB. Period of sinx and cosx = 2π; tanx = π.

Key Formulas

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
sin(A+B) = sinAcosB + cosAsinB
cos(A+B) = cosAcosB − sinAsinB
sin 2A = 2 sinA cosA
cos 2A = cos²A − sin²A

Frequently Asked Questions

What is the general solution of sin θ = 0?: sin θ = 0 when θ = 0, π, 2π, −π, −2π, ... i.e., at all multiples of π. General solution: θ = nπ where n ∈ Z (any integer). Similarly, cos θ = 0 gives θ = (2n+1)π/2; tan θ = 0 gives θ = nπ.
How do you find sin 75° using compound angle formula?: sin 75° = sin(45° + 30°) = sin45°·cos30° + cos45°·sin30° = (1/√2)·(√3/2) + (1/√2)·(1/2) = √3/(2√2) + 1/(2√2) = (√3+1)/(2√2) = (√6+√2)/4.
What is the range of sin x and cos x?: Both sin x and cos x have a range of [−1, 1] — they can only take values between −1 and 1 inclusive. The domain is all real numbers R. Period = 2π. Maximum value 1 at x = π/2 (sin) and x = 0 (cos); minimum value −1 at x = 3π/2 (sin) and x = π (cos).

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