5.5 circular functions: graphs and properties mon nov 10 do now evaluate 1) sin pi/2 2) cos 2pi 3)...
TRANSCRIPT
5.5 Circular Functions: Graphs and PropertiesMon Nov 10
Do NowEvaluate
1) Sin pi/22) Cos 2pi3) Tan pi/4
Circular Functions
• The domains of the trigonometric functions have been sets of angles or rotations.
• Trigonometric functions with domains composed of real numbers (radians) are called circular functions
Reflections on the Unit Circle
• Because the unit circle is symmetric, we can use the coordinates of one point on the unit circle to find coordinates of its reflections
• (Draw unit circle with point x,y )
Ex1
• The point (3/5, 4/5) lies on the unit circle. Find its reflections across the x-axis, y-axis, and origin
Finding Function Values
• Knowing the coordinates of only a few points on the unit circle + reflections allows you to find many trig values
Calculator and Radians
• When working in radians, make sure the calculator is set to radians mode!
• MODE -> RADIANS should be highlighted
Graphs of Sine and Cosine Functions
• One characteristic about circular functions is that they repeat, or oscillate
• Since circular functions travel on a circle, they tend to repeat every revolution
Domain and Range
• The domain and range of both sine and cosine functions are the same
• Domain = All real numbers• Range = [-1, 1]
Period of sine and cosine
• A function with a repeating pattern is called periodic. All trig graphs are periodic.
• The period of y = sin x and y = cos x is 2pi
Amplitude
• The amplitude of a periodic function is defined as one half of the distance between its maximum and minimum values
• You can calculate this by dividing the range by 2
• The amplitude of y = sin x and y = cos x is 1
Symmetry
• Sin (-x) = - sin x• The sine function is odd
• Cos (-x) = cos x• The cosine function is even
Closure
• Describe the graphs of the sine and cosine functions. How are they similar? Different?
• HW: p.505 #1-43 odds