Question

Find the trigonometric ratios for an angle using a reference angle calculator:

a) Sin(θ)
b) Cos(θ)
c) Tan(θ)
d) Cot(θ)

Answer 1

Trigonometry involves finding ratios such as sin(θ), cos(θ), tan(θ), and cot(θ), which relate the angles to the sides of a right-angled triangle. The trigonometric ratios such as sin(θ), cos(θ), tan(θ), and cot(θ) are determined by the ratios of different sides of a right triangle.

Step-by-step explanation:

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of right-angled triangles. The trigonometric ratios such as sin(θ), cos(θ), tan(θ), and cot(θ) are determined by the ratios of different sides of a right triangle.

For any angle θ in a right triangle:

• The sine of θ, written as sin(θ), is the ratio of the length of the opposite side to the length of the hypotenuse.
• The cosine of θ, symbolized as cos(θ), is the ratio of the length of the adjacent side to the hypotenuse.
• The tangent of θ, represented by tan(θ), is the ratio of the length of the opposite side to the adjacent side.
• The cotangent of θ, denoted as cot(θ), is the reciprocal of the tangent, or the ratio of the length of the adjacent side to the opposite side,

By understanding these fundamental trigonometric ratios, solving problems involving right triangles and calculating directions or angles becomes much easier.