Trigonometric Functions The Unit Circle 4 2 Unit
- Slides: 13
Trigonometric Functions: The Unit Circle 4. 2
Unit Circle • The unit circle is a circle of radius 1 with its center at the origin.
Definitions of the Trigonometric Functions in Terms of a Unit Circle If t is a real number and P = (x, y) is a point on the unit circle that corresponds to t, then
Points on the Unit Circle
Example Use the Figure to find the values of the trigonometric functions at t= /2. Solution: The point P on the unit circle that Corresponds to t= /2 has coordinates (0, 1). We use x=0 and y=1 to find the Values of the trigonometric functions
The Domain and Range of the Sine and Cosine Functions • The domain of the sine function and the cosine function is the set of all real numbers • The range of these functions is the set of all real numbers from -1 to 1, inclusive.
Evaluating Trigonometric Functions • Evaluate the six trig functions at each real number. (a) t=л/6 (b) t=5 л/4 (c) t=0 (d) t=л
Evaluate the 6 Trig Functions at t=-л/3
Even and Odd Trigonometric Functions The cosine and secant functions are even. cos(-t) = cos t sec(-t) = sec t The sine, cosecant, tangent, and cotangent functions are odd. sin(-t) = -sin t csc(-t) = -csc t tan(-t) = -tan t cot(-t) = -cot t
Example • If sin t = 2/5 and cos t = 21/5, find the remaining four trig functions
Definition of a Periodic Function A function f is periodic if there exists a positive number p such that f(t + p) = f(t) For all t in the domain of f. The smallest number p for which f is periodic is called the period of f.
Periodic Properties of the Sine and Cosine Functions sin(t + 2 ) = sin t and cos(t + 2 ) = cos t The sine and cosine functions are periodic functions and have period 2. sin = sin 3
Periodic Properties of the Tangent and Cotangent Functions tan(t + ) = tan t and cot(t + ) = cot t The tangent and cotangent functions are periodic functions and have period . tan = tan 2
- Unit circle radians
- Trigonometric functions unit circle approach
- Trigonometric functions unit circle approach
- Graphing rational functions cheat sheet
- Trigonometry cofunction
- Three basic trigonometric functions
- Partner of sine and cosine
- How to find period from sine graph
- 12-7 graphing trigonometric functions answers
- 12-1 trigonometric functions in right triangles
- Implicit differentiation trigonometry
- 9-5 practice graphing trigonometric functions
- Domain and range of trigonometric function
- Trigonometric limit identities