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Trig Summary Sheet :checkered_flag: (units 3 and 4), Relationship: One…
Trig Summary Sheet :checkered_flag: (units 3 and 4)
Trig Terminology
unit circle: a circle with radius of 1 unit used to compare ratios
trigonometric identities: trigonometric statements that are always true
theta(θ): a Greek symbol used to denote the unknown value of an angle
phase shift: the horizontal translation of a sinusoidal functions
csc, sec, cot: secondary trig ratios (reciprocal)
A: vertical stretch/comp. B: horizontal stretch/comp. C: phase shift D: vertical displacement
cos,sine,tan: primary trig ratios
period: the length of one cycle | amplitude: the vertical distance between the max or min and the LOE
Co-terminal angles: any angle±360n
line of equilibrium (LOE): the y average of the max and min y value
Radians: the ratio of the arc length to the radius
Converting from radians to degrees
180/π
Converting form degrees to radians
π/180
Unit Circle
the unit circle represents the change in the 3 primary trig ratios
As you go around the circle the change in the value of the ratios are modeled by the function
The sine function for example gets closer to one as the terminal arm approaches 90 degrees. Then, falls to 0 as the terminal arm approaches 180 degrees
This idea of going around the unit circle explains the graphs of the other ratios as well
Special Triangles
30-60-90
We use special triangles to be able to easily solve the ratios sine, cosine and tangent if you know the value of θ by looking at the lengths of the corresponding sides
45-45-90
Terminal Ray Diagram
The related angel is commonly called alpha (α)
Ratios are always calculated with reference to the acute angle formed between the terminal arm and the x-axis
angles are always calculated starting at 0 degrees and going counter-clockwise
Trig Functions
the graph of the 3 primary trig functions
the base equation for transformations is y=Asin[B(x-C)+D
the same transformation rules apply as transforming the base functions in unit 2
the sin and cos functions model the same curve but their starting points are different
CAST Rule
when trying to find the value of theta in an equation, the CAST rule is used to find which quadrants the terminal arm is in
CAST also applies for secondary trig ratios as the sign doesn't when reciprocating
Trig Identities
some important identities are the Pythagorean identity and the quotient identity
sin²θ+cos²θ=1
tanθ=sinθ/cosθ
they are used to solve trigonometric equations as all identities are true
Relationship: One full revolution is 2π
θ=a/r
θ=2πr
θ=2π
