Trigonometric Ratio Calculator

This Trigonometric Ratio Calculator helps you find the values of sine, cosine, and tangent in a right triangle using the correct side lengths. It uses the formulas sin(θ) = opposite / hypotenuse, cos(θ) = adjacent / hypotenuse, and tan(θ) = opposite / adjacent. Choose the ratio you want, enter the two required side lengths, and the calculator will work out the result. It is a simple way to check answers, understand trigonometric ratios, and practise basic trigonometry step by step.

Step-by-step method

1. Identify what is given.
2. Write the correct ratio.
3. Substitute the values and divide.

Formulas:

Formula: sin(θ)

Formula: cos(θ)

Formula: tan(θ)

Example 1: sin(θ) with opposite = 3, hypotenuse = 5

Step 1 - Identify what is given.

In this problem: The given values are opposite = 3 and hypotenuse = 5.

Step 2 - Write the correct ratio.

In this problem: Use the ratio: sin(θ) = opposite / hypotenuse.

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: sin(θ) = 3 ÷ 5 = 0.6.

Final answer: sin(θ) = 0.6

Example 2: tan(θ) with opposite = 3, adjacent = 4

Step 1 - Identify what is given.

In this problem: The given values are opposite = 3 and adjacent = 4.

Step 2 - Write the correct ratio.

In this problem: Use the ratio: tan(θ) = opposite / adjacent.

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: tan(θ) = 3 ÷ 4 = 0.75.

Final answer: tan(θ) = 0.75