Trigonometric ratios for 30°, 45° and 60°

Understanding Trigonometric Ratios

Trigonometry studies the relationship between the angles and sides of a triangle. The three most common ratios used are sine (sin), cosine (cos) and tangent (tan).
The trigonometric ratios are usually represented as sinθ, cosθ, and tanθ, where θ represents an angle.
For a right-angled triangle, you can calculate these ratios using the lengths of the sides: sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent.

Trigonometric ratios for 30°, 45°, and 60°

These particular angles are frequently encountered. Here are the key trigonometric values to remember:

30 Degrees - (π/6 Radians)

sin 30° = 0.5
cos 30° = √3/2 (approximately 0.87)
tan 30° = √3/3 (approximately 0.58)

45 Degrees - (π/4 Radians)

sin 45° = √2/2 (approximately 0.71)
cos 45° = √2/2 (approximately 0.71)
tan 45° = 1

60 Degrees - (π/3 Radians)

sin 60° = √3/2 (approximately 0.87)
cos 60° = 0.5
tan 60° = √3 (approximately 1.73)

Applications of Trigonometric Ratios

These ratios are often used for solving triangles — finding missing sides or angles.
Trigonometric ratios can be applied in various fields like physics, engineering, or geography to solve practical problems related to distance, height, or directions.

Remember that a good understanding of these ratios and their use is key to successfully answering problems related to right-angled triangles. It is also important to keep practicing a variety of problems to enhance understanding.