Study Flashcards
When is cos 0?
Every π/2
0 every π/2
cos
When is sin 0?
Every π
0 every π
sin
What kind of functions are sin and cos?
sin is odd and cos is even
Periods of sin and cos
2π
2π is the period of
sin and cos
Form of sinusoidal function
f(x) = a sin[b(x-c)] + d
or
f(x) = a cos[b(z-c)] + d
f(x) = a sin[b(x-c)] + d
or
f(x) = a cos[b(z-c)] + d
Sinusoidal functions
What is the range of y = a sinx and y = a cosx?
(-a,a)
(-a,a)
Range of y = a sinx and y = a cosx
What is the period of y =sinbx or
y = cosbx
2π/b
2π/b
period of y =sinbx or
y = cosbx
With sinusoidal functions, a horizontal shift is called
Phase shift
Phase shift
Horizontal shift in sinusoidal function
If a < 0 in a sinusoidal function
|a| is amplitude and function is reflected across x-axis
|a| is amplitude and function is reflected across x-axis
If a < 0 in sinusoidal function
What is the cycle of a graph
x values for which one complete repetition of the graph is completed
x values for which one complete repetition of the graph is completed
Cycle
Domain and range of tan graph
Every number except intervals of π/2 and range is all reals
Zeros of tan function
Every π
Has zeros at every π
Tan function
For tan graphs, divide interval into equal parts of length
1/4 • π/b
1/4 • π/b
Tan graph intervals
Locate adjacent asymptotes
b(x-c)=-π/2 and b(x-c)= π/2
b(x-c)=-π/2 and b(x-c)= π/2
Locate adjacent asymptotes
Domain and range of csc x
Domain: asymptote every π
Range: (-∞,-1] U [1, ∞)
Domain: asymptote every π
Range: (-∞,-1] U [1, ∞)
csc x
Domain and range of sec x
Domain: asymptote every π/2
Range: (-∞,-1] U [1, ∞)
Domain: asymptote every π/2
Range: (-∞,-1] U [1, ∞)
Domain and range of sec x
Even or odd?:
csc, sec, cot
Odd, even, odd
Inverse function is defined by
y = sin^-1x iff x = siny
y = sin^-1x iff x = siny
Inverse function
x = siny for
-1 <= x <= 1 and -π/2 <= y <= π/2
y = cos^-1x iff x = cos y for
-1 <= x <= 1 and 0 <= y <= π
-1 <= x <= 1 and 0 <= y <= π
y = cos^-1x iff x = cos y for
y = tan^1 x iff x = tan y for
All reals and -π/2 <= y <= π/2
All reals and -π/2 <= y <= π/2
y = tan^1 x iff x = tan y for
Why is cos^-1[cos(5π/4)] 3π/4?
Because arccos can only be in second quadrant or first and subtracting π from 5π/4 gives a reference angle in the second quadrant
How are the intervals of a graph identified?
Divide period by 4
Divide period by 4
Identifying intervals of a graph
