Trigonometric Identities
Reciprocal Identities
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Midline
the horizontal dilation of the sinusoidal function by a factor of 1/b
Concave Up
The graph of a function is concave up on intervals in which the rate of change is increasing.
Arithmetic Sequence
Successive terms in an arithmetic sequence have a common difference, and a constant rate of change.
an =a0+dn
Pythagorean Identities
sin²(θ) + cos²(θ) = 1
1 + tan²(θ) = sec²(θ)
1 + cot²(θ) = csc²(θ)
Period
the period of the sinusoidal function is 2π/|b|
Concave Down
The graph of a function is concave down on intervals in which the rate of change is decreasing.
Geometric Sequence
Successive terms in a geometric sequence have a common ratio, and a constant proportional change.
gn =g0 ∙ rn
Double Angle Identities
sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
Amplitude
he amplitude of the sinusoidal function is |a|
Tandem
The input and output values of a function vary in tandem according to a function, which is expressed graphically, numerically, analytically, or verbally.
Sequence
A sequence is a function with domain of whole (natural) numbers and range of real numbers.
Sum & Difference Identities
sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β)
cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β)
tan(α ± β) = (tan(α) ± tan(β)) / (1 ∓ tan(α)tan(β))
Horizontal Dilation
, the horizontal dilation of the sinusoidal function by a factor of 1/b
Concave Up
When the AROCs over equal-length input-value intervals are INCREASING for all small-length intervals, the graph of the function is concave up.
Composite Function
For functions f and g the composite function f(g(x)) maps a set of input values (from g) to a set of output values (from f). There can be domain
restrictions on g, so those same domain restrictions also apply to f(g(x)). There might also be domain restrictions to f(g(x)) depending on the output values from g.