Sine, cosine, and tangent are important math functions. They help us understand angles and sides in right triangles.

1. What They Mean:

   • Sine ($\sin$): For an angle called $\theta$, the sine is found by this formula: $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}.$ This means you take the length of the side opposite the angle and divide it by the longest side of the triangle.

   • Cosine ($\cos$): For the same angle $\theta$, the cosine is calculated like this: $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}.$ Here, you take the length of the side next to the angle and divide it by the longest side.

   • Tangent ($\tan$): The tangent connects sine and cosine using this formula: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \frac{\text{opposite side}}{\text{adjacent side}}.$ So, the tangent shows the ratio of the opposite side to the adjacent side.

2. Pythagorean Identity: There is an important rule called the Pythagorean identity. It states that: $\sin^2(\theta) + \cos^2(\theta) = 1.$ This means if you square the sine and cosine of an angle and add them together, you always get 1.

These ideas help us get ready for more advanced topics in trigonometry later on!