- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
Here's how to use SOH-CAH-TOA to find the value of a trigonometric ratio:
1. Identify the opposite, adjacent, and hypotenuse sides of the right triangle.
- The opposite side is the side opposite the angle you are interested in.
- The adjacent side is the side adjacent to the angle you are interested in.
- The hypotenuse is the longest side of the triangle, and it is opposite the right angle.
2. Write down the trigonometric ratio you are looking for.
- Sine, cosine, or tangent
3. Substitute the values of the opposite, adjacent, and hypotenuse sides into the trigonometric ratio.
- Make sure to use the correct units (e.g., degrees or radians)
4. Calculate the value of the trigonometric ratio.
- Use a calculator or trigonometric table to find the value of the trigonometric ratio.
5. Label the answer with the appropriate trigonometric symbol (sin, cos, or tan)
Here are some examples of how to use SOH-CAH-TOA:
* To find the sine of 30 degrees, we look at the opposite side of the 30-degree angle, which is 3, and the hypotenuse, which is 5. So sin(30°) = 3/5.
*To find the cosine of 45 degrees, we look at the adjacent side of the 45-degree angle, which is 4, and the hypotenuse, which is 5. So cos(45°) = 4/5.
* To find the tangent of 60 degrees, we look at the opposite side of the 60-degree angle, which is 6, and the adjacent side, which is 3. So tan(60°) = 6/3 = 2.
