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:

Example 1:

Step 1 - Identify what is given.

In this problem: The given values are \(\text{opposite} = 3\) and \(\text{hypotenuse} = 5\).

Step 2 - Write the correct ratio.

In this problem: Use the ratio: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: \(\sin(\theta) = \frac{3}{5} = 0.6\).

Final answer:

Example 2:

Step 1 - Identify what is given.

In this problem: The given values are \(\text{opposite} = 3\) and \(\text{adjacent} = 4\).

Step 2 - Write the correct ratio.

In this problem: Use the ratio: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: \(\tan(\theta) = \frac{3}{4} = 0.75\).

Final answer:

See Example 1 Hide Example 1

Problem

\(\sin(\theta) \text{ with } \text{opposite} = 3,\; \text{hypotenuse} = 5\)

Approach

Step-by-step method

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

Step 1

Step 1 - Identify what is given.

In this problem: The given values are \(\text{opposite} = 3\) and \(\text{hypotenuse} = 5\).

\(\text{opposite} = 3,\; \text{hypotenuse} = 5\)

Step 2

Step 2 - Write the correct ratio.

In this problem: Use the ratio: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).

\(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step 3

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: \(\sin(\theta) = \frac{3}{5} = 0.6\).

\(\sin(\theta) = \frac{3}{5} = 0.6\)

Final Answer

\(\sin(\theta) = 0.6\)

See Example 2 Hide Example 2

Problem

\(\tan(\theta) \text{ with } \text{opposite} = 3,\; \text{adjacent} = 4\)

Approach

Step-by-step method

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

Step 1

Step 1 - Identify what is given.

In this problem: The given values are \(\text{opposite} = 3\) and \(\text{adjacent} = 4\).

\(\text{opposite} = 3,\; \text{adjacent} = 4\)

Step 2

Step 2 - Write the correct ratio.

In this problem: Use the ratio: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).

\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)

Step 3

Step 3 - Substitute the values and divide.

In this problem: Substitute and divide: \(\tan(\theta) = \frac{3}{4} = 0.75\).

\(\tan(\theta) = \frac{3}{4} = 0.75\)

Final Answer

\(\tan(\theta) = 0.75\)