Unit 3

Question 1

The horizontal length of one cycle of a periodic or repeating function is called the…?

Answer 1

period

Question 2

Half the difference between the maximum and the minimum values of a periodic function is known as the…

Answer 2

amplitude

Question 3

positive angles are rotated in this direction

Answer 3

counterclockwise

Question 4

given point P on a unit circle, the sine of the angle is the __-coordinate of point P

Answer 4

y-coordinate

Question 5

domain and range for f(theta)=sin(theta)
f(theta)=cos(theta)

Answer 5

domain: all real numbers
range: [-1,1]

Question 6

The period and frequency of a sinusoidal function are ____. State both period and frequency for sine and cosine

State the equations, not the actual number

Answer 6

reciprocals
period: 2pi/b
frequency: b/2pi

Question 7

For any function in the form:
f(x)=asin[b(theta+c)]+d or f(x)=acos[b(theta+c)]+d. Explain the transformations for a,b,c,d

Answer 7

a: vertical dilation by a factor of a (affects y-value)
b: horizontal dilation by a factor of 1/b (affects x-value)
c: horizontal translation, or phase shift, by theta=-c (affects x-value)
d: vertical translation, including its midline (affects y-value)

Question 8

State the period of the tangent function

Answer 8

pi

the terminal ray slope repeats every one-half revolution of the circle

Question 9

In order to define their respective inverse trigonometric functions, state the domain restrictions for sinx, cosx, and tanx

Answer 9

sin: [–pi/2, pi/2]
cos: [0,pi]
tan: (–pi/2, pi/2)

Question 10

The secant, cosecant, and cotangent functions are reciprocals of…

Answer 10

secant: cosine
cosecant: sine
cotangent: tangent

Question 11

State the Pythagorean Identities applied to right triangles with points on the unit circle at coordinates (cos(theta), sin(theta))

Answer 11

sin^2(theta) + cos^2(theta) = 1
tan^2(theta) = sec^2(theta) -1
sin^2(theta) = 1-cos^2(theta)
cos^2(theta) = 1-sin^2(theta)
1+cot^2(theta) = csc^2(theta)

Question 12

State the sum and difference identities for sin

Answer 12

sin(a+b) = sinAcosB+cosAsinB
sin(a-b) = sinAcosB-cosAsinB

Question 13

State the sum and difference identities for cosine

Answer 13

cos(a+b)=cosAcosB-sinAsinB
cos(a-b)=cosAcosB+sinAsinB

Question 14

The coordinates of a point in the polar coordinate system (r,theta) can be converted to coordinates in the rectangular system using…

Answer 14

Convert (x,y) to (r,theta)
x=rcos(theta)
y=rsin(theta)

Question 15

The coordinates of a point in the rectangular coordinate system (x,y) can be converted to coordinates in the polar system using…

Answer 15

convert (r,theta) to (x,y)
r= sqrtx^2+y^2

Question 16

If a polar function is positive and increasing or negative and decreasing, then the distance between f(theta) and the origin is…

Answer 16

increasing

Question 17

If a polar function is positive and decreasing or negative and increasing, then the distance between f(theta) and the origin is…

Answer 17

decreasing