The Trig Functions
The three main trigonometric ratios relate the angles of a right triangle to the lengths of its sides. They are sine, cosine, and tangent.
For a given angle $\theta$ in a right triangle:
- **Sine** ($sin(\theta)$) is the ratio of the **opposite** side to the **hypotenuse**.
- **Cosine** ($cos(\theta)$) is the ratio of the **adjacent** side to the **hypotenuse**.
- **Tangent** ($tan(\theta)$) is the ratio of the **opposite** side to the **adjacent** side.
A common mnemonic to remember these is **SOH CAH TOA**.
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Video: The Unit Circle & Graphs!
Watch this video to visualize how trig ratios relate to the unit circle and create their characteristic wave-like graphs. 🌊
Practice Problems
Find the values of the trig ratios and key properties of their graphs!
1) In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is $sin(\theta)$? (e.g., 3/5)
2) What is the period of the function $y = sin(x)$?
3) What is the amplitude of the function $y = 3cos(x)$?
4) What is the value of $sin(90°)$?
⚡ Trig Speed Quiz
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