Pesky Unit Circle
Sin(90)
1
Remember sin is verticality and 90 degrees is the highest point on the unit circle
Even vs Odd Functions
even functions are symmetrical across the Y axis whereas odd functions are rotationally symmetric 180* about the origin
Factor x2+5x+4
(x+4)(x+1)
sin (x has a zero term of what number)
0
sin waves have a zero term of 0 unless manipulated by a phase shift or vertical shift or amplitude change
What does sin2x=?
2 · sin · cos
Sin(150)
1/2
even though the degree is high, the verticality of that point is still small
Convergent vs Divergent
A convergent function will approach a number forever and ever and will never reach with, while divergent functions approach +/- infinity
x2-3x+2
(x-2)(x-1)
Cos (x) has a 0 term of what number
1
cos waves have a zero term of 1 unless manipulated by a phase shift or vertical shift or amplitude change
What does the cos2x=?
cos2x-sin2x
1-2sin2x
2cos2x-1
Sin(4∏/3)
-√3/2
What method should you use when multiplying two binomials together
FOIL
x2-12x-13
(x-13)(x+1)
what is the amplitude of this graph
y=2sin(3x/4)+5
2
the amplitude is always the value in front of the sin/cos
Sin(a-b)=?
sin(a)·cos(b)-cos(a)·sin(b)
remember, when its sin, the sign stays the same!
Sin(1495871∏)
0
The sin will always be zero if it is a whole number of ∏ and the cos will either be +/- 1
Does (x+y)2=x2+y2
NOOO, it equals x2+2xy+y2
5x2+50x+120
5(x-6)(x-4)
Is an upwards facing parabola convergent or divergent?
divergent, the end behavior of both ends is where x approaches infinity y approaches infinity
cos(A+B)=?
cos(A)·cos(B)-sin(A)·cos(B)
Remember, when its cos the sign changes
Sin(225)
-√2/2
what is sin2x+cos2x?
1
pythagorean identity!
24x2-6xy-9y2
3(2x+y)(4x-3y)
what is the right end behavior of the exponential decay graph y=0.5x
it is convergent towards 0 because it will get closer and closer but never touch the x axis
cos(x/2)=?
±(√(1+cosx)/2)
remember that the cos identity is positive while the sign identity goes negative