Math : Unit 6

Trigonometric Functions

How do you find the period in a trig graph?

b/2pi or b/pi

How to find the starting point for a sin/cos/sec/csc

Set whatever is INSIDE the parenthesis equal to 0

How to find the ending point for sin/cos/sec/csc

Set whatever is inside the parenthesis equal to 2pi

How do you find the other points in a graph?

Divide the period by 4 and add that value to the starting point

What is special about a cos or sec graph

The second and fourth points have the midline value as their y-coordinate

What is special about a sin or csc graph?

The first, third, and fifth points have the midline value as their y-coordinate

What is important about the waves in a sec or csc graph

If the point falls above the midline, it curves upwards and if it falls below the midline, it curves downwards

How to find the starting point for a tan graph?

Set the parenthesis equal to - pi/2

How to find the end point of a tan graph

Set the parenthesis equal to pi/2

How to find the starting point for cot?

Set the parenthesis equal to 0

How to find the ending point for cot?

Set the parenthesis equal to pi

What is special about the first and last points of a cot/tan graph?

They are undefined

What is special about the 4th and 2nd points of a cot/tan graph?

They must be -1 or 1

How to find the y-value for reg points?

Plug in the x coordinate in the parenthesis, find the value, and look for the value on the unit circle as (sin,cos) or for tan, y/x and for cot, x/y

What are the points for 30,45, and 60 (first quadrant) on the unit circle?

30 : (√3/2, 1/2) 45 : (√2/2, √2/2) 60 : (1/2, √3/2)

What are the points for 210,225, and 240 (third quadrant) on the unit circle?

210 : (-√3/2, -1/2) 225 : (-√2/2, -√2/2) 240 : (-1/2, -√3/2)

What are the points for 300,315, and 330 (first quadrant) on the unit circle?

300 : (1/2, -√3/2) 315 : (√2/2, -√2/2) 330 : (√3/2, -1/2)

What are the points for 120,135, and 150 (second quadrant) on the unit circle?

120 : (-1/2, √3/2) 135 : (-√2/2, √2/2) 150 : (-√3/2, 1/2)