Trigonometric Functions

Question 1

What do maximum and minimum mean when talking about periodic functions?

Answer 1

The top or the crest and the bottom of the trough for each period.

Question 2

What does period mean when talking about periodic functions?

Answer 2

The length of one cycle (or repetition). So it’s the distance between any two repeating points on the function.

Question 3

What does amplitude mean (when talking about functions)?

Answer 3

The distance from the midpoint (principal axis) to the highest or lowest point of the function.

Question 4

What do maximum and minimum mean when talking about periodic functions?

Answer 4

The top or the crest and the bottom of the trough for each period.

Question 5

How do you find the tangent of an angle that is *not* part of a right triangle?

Answer 5

Question 6

What is the period of the following functions?

y=AsinB(x-C)+D

y=AcosB(x-C)+D

Answer 6

Question 7

What is the amplitude of the following functions?

y=AsinB(x-C)+D

y=AcosB(x-C)+D

Answer 7

The absolute value of A.

|A|

Question 8

What horizontal translation is applied to the standard sine/cosine functions when using the form below?

y=Asin(B(x-C))+D

y=Acos(B(x-C))+D

Answer 8

The functions are shifted right by C.

Question 9

What vertical translation is applied to the standard sine/cosine functions when using the form below?

y=AsinB(x-C)+D

y=AcosB(x-C)+D

Answer 9

The functions are shifted up by D.