Calculus I

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Trigonometric functions

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Calculus I

Definition

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They are fundamental in studying periodic phenomena and in calculus for analyzing oscillatory behaviors.

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5 Must Know Facts For Your Next Test

  1. The primary trigonometric functions are sine ($\sin$), cosine ($\cos$), and tangent ($\tan$).
  2. $\sin(\theta) = \frac{opposite}{hypotenuse}$, $\cos(\theta) = \frac{adjacent}{hypotenuse}$, and $\tan(\theta) = \frac{opposite}{adjacent}$. These ratios define the basic trigonometric functions.
  3. The unit circle is a key concept for understanding trigonometric functions, where $x$-coordinates represent $\cos(\theta)$ and $y$-coordinates represent $\sin(\theta)$.
  4. Trigonometric identities such as $\sin^2(x) + \cos^2(x) = 1$ are crucial for simplifying expressions and solving equations.
  5. Inverse trigonometric functions (like $\arcsin$, $\arccos$, and $\arctan$) are used to find angles when given function values.

Review Questions

  • What are the definitions of sine, cosine, and tangent in terms of a right triangle?
  • How does the unit circle help in understanding the values of trigonometric functions?
  • State and prove one fundamental trigonometric identity.
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