Day 3-Trigonometry-Graphs of Sine and Cosine

Hey whatsup everybody it's me Emmanuel from your Pre-Cal30S class. Today I'm going to talk about what we learned in class yesterday from the beginning of our Trigonometry Unit. We learned about Graphing Sine and Cosine values, Comparing Graphs of Sine and Cosine Values, and naming the Five Key Points
of Sine and Cosine.

The basic equations of Graphing Sine and Cosine are y= a sin bx, y= a cos bx

The intermediate equations for Transformation of Graphing Sine and Cosine are y= a sinb(x-h)+k , y= a cosb (x-h)+k , h
represents the horizontal movement of the graph and k represents the vertical movement of the graph.

Amplitude- The amplitude is the distance from the x-axis to the highest point or lowest point for a sin x or cos x function, and is
unlimited for a tan x function.

A period is the length of a cycle which is measured in degrees or radians.

The periods of a sin x or cos x function is 360°

The period for a tan x function is 180°


II-these brackets represent the absolute value of a function. Absolute Value means that whichever number is between the brackets becomes positive.

The domain of a function is a set of numbers with all first x-coordinates of the ordered pairs in a function.

The range of a function is a set of numbers with all first y coordinates of the ordered pairs in a function.

The maximum value is the highest point of a function and the minimum value is the lowest point on the curve of the function, they are represented by
y-values.

For the basic graph of y=sin x


Domain: (-∞,∞)

Range: [-1, 1]

Period: 360°

Maximum Value: y = 1

Minimum Value: y = -1

X-intercept: x = c180°


For the basic graph of y=cos x


Domain: (-∞,∞)

Range: [-1,1]

Period: 360°

Maximum Value: y = 1

Minimum Value: y = -1

X-intercept: x = c180°-90°