OBJECTIVE 4: THE SIX TRIG FUNCTIONS

Question 1

The six trigonometric ratios:

Answer 1

Sine, cosine, tangent, cosecant, secant, and cotangent

Question 2

Sine

Answer 2

The y-value of coordinates on the Unit Circle.
Can be found also by y/r

Question 3

Cosine

Answer 3

The x-value of coordinates on the unit circle.

Can also be found as x/r

Question 4

Tangent

Answer 4

The ratio of sine/cosine

Also, y/x.

Question 5

Cosecant

Answer 5

The reciprocal of sine.

1/sine

1/y

Question 6

Secant

Answer 6

The reciprocal of cosine.

1/cos

1/x

Question 7

Cotangent

Answer 7

The reciprocal of tangent

cos/sin

x/y

Question 8

Name the function

Answer 8

Cotangent

Question 9

Name the function

Answer 9

Secant

Question 10

Name the function

Answer 10

Cosecant

Question 11

Name the function

Answer 11

Tangent

Question 12

Name the function

Answer 12

Cosine

Question 13

Name the function

Answer 13

Sine

Question 14

Amplitude

Answer 14

The distance from the midline to peaks (max/min) of the function

Question 15

Midline

Answer 15

The horizontal line that marks the vertical shift, or middle value of a function

Question 16

Period Length

Answer 16

The width of one cycle of a trig function

Question 17

Frequency

Answer 17

The amount of times a function repeats its cycles from 0 to 2pi (or 0 to pi for tangent/cotangent)

Question 18

Phase shift

Answer 18

The horizontal shift (rigid) of a trig function

Question 19

Period Length (formula)

Answer 19

T = 2pi / frequency (for sine, cosine, cosecant, and secant)

T = pi / frequency (for tangent and cotangent)

Question 20

Frequency formula

Answer 20

Frequency = 2pi / period (for sine, cosine, cosecant, and secant)

Frequency = pi / period (for tangent and cotangent)

Question 21

Conversion from Radians to degrees

Answer 21

Replace pi with 180 degrees.

Ex) 3pi / 4 = (3/4)(180) = 135

Question 22

Conversion from degrees to radians

Answer 22

Express as a fraction of 180 and multiply by pi radians.

Ex) 45degrees = (45/180)*pi = (1/4)*pi = pi/4

Question 23

Pythagorean Identity #1

Answer 23

sin^2(theta) + cos^2(theta) = 1

Question 24

Pythagorean Identity #2

Answer 24

1 + cot^2(theta) = csc^2(theta)

Question 25

Pythagorean Identity #3

Answer 25

tan^2(theta) + 1 = sec^2(theta)

Question 26

Context of Sinusoidal Functions:

Amplitude

Answer 26

The variation from the median. Example, the radius of a ferris wheel could represent how far above and below the axle height a person is depending on time.

Question 27

Context of Sinusoidal Functions:

Midline

Answer 27

The central value of a periodic pattern. In a ferris wheel, it could be represented by the height of the axle off of the ground.

Question 28

Context of Sinusoidal Functions:

Period

Answer 28

The length of time it takes to complete one full cycle of a periodic situation.

Ex) season length, lunar phases, time for one revolution of a ferris wheel