Trigonometry

In a right

In a right-angled triangle, we identify three sides relative to any acute angle: the hypotenuse (longest side opposite to 90°), the opposite side (sid

Three fundamental ratios

Three fundamental ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. These ratios remain constant for simila

For complementary angles (angles that add

For complementary angles (angles that add up to 90°): sin θ = cos(90° - θ), cos θ = sin(90° - θ), and tan θ × tan(90° - θ) = 1. Also, sin θ/cos θ = ta

Specific trigonometric values for 0°

Specific trigonometric values for 0°, 30°, 45°, 60°, and 90° derived from special triangles: 30°-60°-90° triangle and 45°-45°-90° isosceles triangle.

30°

30°-60°-90° triangle has sides in ratio 1:√3:2, and 45°-45°-90° triangle has sides in ratio 1:1:√2. These ratios help derive standard trigonometric va