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What is Sine?
 Sine = Opposite_
 Hypotenuse
i.e. sin(θ) = a/h

What is Cosine?
 Cosine = Adjacent
 Hypotenuse
i.e. cos(θ) = b/h


a) What is secant?
b) What is cosecant?
c) What is cotangent?

Unit circle (with degree/radian angles and corresponding point values)

How many degrees is radians?
360°
Thus, 1 radian =

What are the radians, sine, and cosine equivalent for 0°?
 Radians: 0
 Sine: 0
 Cosine: 1

What are the radians, sine, and cosine equivalent for 30°?

What are the radians, sine, and cosine equivalent for 45°?

What are the radians, sine, and cosine equivalent for 60°?

What are the radians, sine, and cosine
equivalent for 90°?
 Radians:
 Sine: 1
 Cosine: 0

Indicate the signs of sine, cosine, and tangent in quadrant I of the unit circle.

Indicate the signs of sine, cosine, and tangent
in quadrant II of the unit circle.

Indicate the signs of sine, cosine, and tangent
in quadrant III of the unit circle.

Indicate the signs of sine, cosine, and tangent in quadrant IV of the unit circle.


At what point is the xintercept located for the sine function?
 n = any integer (number of cycles)

At what point does the sine function reach a minimum (i.e. 1)?
 n = any integer (number of cycles)

At what point does the cosine function reach a maximum (i.e. +1)?
It reaches a maximum at
 n = any integer (number of cycles)

At what point is the xintercept located for the cosine function?

At what point does the cosine function reach a minimum (i.e. 1)?
n is any integer

What are the corresponding periodicity (function repeats itself) of the following trig functions:
a) tangent & cotangent
b) sine & cosine
 a) periodic
  it also has vertical asymptotes (lines where the function never crosses)
  vert. asymptote at for every odd integer n (where cos is 0 > sin / 0 is undefined)
b) periodic

What is the inverse of a trig function?
It is taking the value of an angle and finding out what the angle is.
 e.g. sin (sin^{1}(x)) = x
 Thus, sin(θ) = x and sin^{1}(x) = θ

Recall 8 trig identities.
a) sin ^{2}θ + cos ^{2}θ = 1
 derived from the Pythagorean Theorem (sin and cos are legs of a triangle while the hyp = radius (1))
b) tan ^{2}θ + 1 = sec ^{2}θ
c) 1 + cot ^{2}θ = csc ^{2}θ
d) sin(2θ) = 2(sinθ)(cosθ)
e) cos(2θ) = 1  2(sin ^{2}θ)
f) tan(2θ) =
g) sin(θ) = sin(θ) < odd function
h) cos(θ) = cos(θ) < even function
Note: recall "odd" and "even" functions:
even: f(x) = f(x) > graph symm. along yaxis
odd: f(x) ≠ f(x) > graph symm. along its origin
instead: f(x) = f(x) or f(x) = f(x)

Recall trig identities for sin(θ) & cos(θ) when adding 2 to a point on the unit circle
cos(θ) = cos(θ + 2 )
sin(θ) = sin(θ + 2 )
Note: 2 is just one full cycle.

Recall trig function (sum or diff. of two angles) for sine:
sin (x + y) = ?
sin (x  y) = ?
 sin (x + y) = sin(x)cos(y) + cos(x)sin(y)
 sin (x  y) = sin(x)cos(y)  cos(x)sin(y)
Mnemonic: sine is "sum"thing that switches :)
** start with a "+" (or "") > stays with a "+" (or "") on the other equation.

What is the tangent addition formula > tan(α + β)?

Recall trig function (sum/diff of two angles) for cosine:
cos (x + y) = ?
cos (x  y) = ?
 cos (x + y) = cos(x)cos(y)  sin(x)sin(y)
 cos (x  y) = cos(x)cos(y) + sin(x)sin(y)
Mnemonic: "opposite" the functions did not "switch."

What are polar coordinates?
A system that uses the hypotenuse of the triangle (r) and the angle from the xaxis (θ).
 instead of two distance components (as in a Cartesian plane x & y), this system use one radial distance component (distance from origin) and an angle component.
 A point is written as the ordered pair (r, θ).

Identities to use to convert points between polar and Cartesian coordinates.
i. r^{2} = x^{2} + y^{2}
ii. x = (r) x (cos(θ))
iii. y = (r) x (sin(θ))

What are the trig properties for Sum or Differences of Two Angles?

What are the trig properties for Cofunction Identities (for radians & degrees)?

What are the trig properties for OddEven Identities?

