Trig ratios for multiples of 30°, 45° and 60°

Trigonometric Ratios for Angles of 30°, 45° and 60°

Ratio for 30°

A 30-degree angle is known as a Pi/6 radian angle in terms of radians.
The sine (sin) of 30° is 1/2. Meaning, in a right-angled triangle, the ratio of the length of the side opposite to the angle over the length of the hypotenuse is 1/2.
The cosine (cos) of 30° is √3/2. It represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.
The tangent (tan) of 30° is 1/√3 or √3/3. This signifies the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in the right-angled triangle.

Ratio for 45°

A 45-degree angle is referred to as a Pi/4 radian angle.
The sin of 45° is √2/2 or 1/√2, which means the length of the side opposite the angle is equal to the length of the side adjacent to the angle in the right-angled triangle.
The cos of 45° is also √2/2 or 1/√2, indicating that the length of the hypotenuse is √2 times the length of either the adjacent or opposite side.
The tan of 45° is 1, which suggests that the length of the side opposite the angle is equal to the length of the side adjacent to the angle for any right-angled triangle.

Ratio for 60°

A 60-degree angle is equivalent to a Pi/3 radian angle in terms of radians.
The sin of 60° is √3/2. It implies that the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right-angled triangle is √3/2.
The cos of 60° is 1/2. It signifies that the length of the adjacent side is half the length of the hypotenuse.
The tan of 60° is √3. It means in a right-angled triangle, the length of the side opposite the angle is √3 times the length of the side adjacent to the angle.

Remember, these trigonometric ratios are crucial in solving geometry problems involving angles of 30°, 45° and 60°. Practice them regularly to solidify your understanding and ability to use them efficiently.