OBJECTIVE 4: THE SIX TRIG FUNCTIONS Flashcards
The six trigonometric ratios:
Sine, cosine, tangent, cosecant, secant, and cotangent
Sine
The y-value of coordinates on the Unit Circle.
Can be found also by y/r
Cosine
The x-value of coordinates on the unit circle.
Can also be found as x/r
Tangent
The ratio of sine/cosine
Also, y/x.
Cosecant
The reciprocal of sine.
1/sine
1/y
Secant
The reciprocal of cosine.
1/cos
1/x
Cotangent
The reciprocal of tangent
cos/sin
x/y
Name the function
Cotangent
Name the function
Secant
Name the function
Cosecant
Name the function
Tangent
Name the function
Cosine
Name the function
Sine
Amplitude
The distance from the midline to peaks (max/min) of the function
Midline
The horizontal line that marks the vertical shift, or middle value of a function
Period Length
The width of one cycle of a trig function
Frequency
The amount of times a function repeats its cycles from 0 to 2pi (or 0 to pi for tangent/cotangent)
Phase shift
The horizontal shift (rigid) of a trig function
Period Length (formula)
T = 2pi / frequency (for sine, cosine, cosecant, and secant)
T = pi / frequency (for tangent and cotangent)
Frequency formula
Frequency = 2pi / period (for sine, cosine, cosecant, and secant)
Frequency = pi / period (for tangent and cotangent)
Conversion from Radians to degrees
Replace pi with 180 degrees.
Ex) 3pi / 4 = (3/4)(180) = 135
Conversion from degrees to radians
Express as a fraction of 180 and multiply by pi radians.
Ex) 45degrees = (45/180)*pi = (1/4)*pi = pi/4
Pythagorean Identity #1
sin^2(theta) + cos^2(theta) = 1
Pythagorean Identity #2
1 + cot^2(theta) = csc^2(theta)
Pythagorean Identity #3
tan^2(theta) + 1 = sec^2(theta)
Context of Sinusoidal Functions:
Amplitude
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.
Context of Sinusoidal Functions:
Midline
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.
Context of Sinusoidal Functions:
Period
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
