📚 Topic Summary
Understanding the domain and range of trigonometric functions is crucial for success in trigonometry and calculus. The domain refers to all possible input values (angles) for which the function is defined, while the range represents all possible output values that the function can produce. This activity will help you solidify your knowledge of the domain and range for all six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
🧮 Part A: Vocabulary
Match the following terms with their definitions:
- Term: Domain
- Term: Range
- Term: Asymptote
- Term: Periodic Function
- Term: Trigonometric Function
- Definition: A function that repeats its values in regular intervals.
- Definition: A function of an angle expressed as a ratio of two sides of a right triangle.
- Definition: The set of all possible output values (y-values) of a function.
- Definition: A vertical line that a curve approaches but never touches.
- Definition: The set of all possible input values (x-values) of a function.
✍️ Part B: Fill in the Blanks
The sine and cosine functions have a domain of all ______ numbers. The tangent function has vertical ______ where cosine equals zero. The range of sine and cosine is between ______ and ______. The secant and cosecant functions are reciprocals of cosine and ______, respectively. The cotangent function is the reciprocal of the ______ function.
🤔 Part C: Critical Thinking
Explain why the tangent function has asymptotes, while the sine function does not.