Trig Flashcards
the x-coordinate of the point t
on the number circle.
cos t
the y-coordinate of the point t
on the number circle.
sin t
Period of Cosine
2pi
Period of Sine
2pi
cis(t) =
cos(t) + isin(t)
Is Cosine an even or odd function
Even
Formula for coterminal angles of cos
cos(t + 2kpi)
Is Sine an even or odd function
Odd
Formula for coterminal angles of sin
Sin(t + 2kpi)
Equation of the Unit Circle
x^2 + y^2 = 1
projection of t through the origin to the s-axis.
Also the slope of the line through the origin and t
tan t
projection of t through the origin to the r-axis.
Also the reciprocal slope of the line through the origin and t
cot t
What is the period of tan
pi
is tangent an even or odd function
odd
cos co-function identity
sin(pi/2 - t)
sin co-function identity
cos(pi/2 - t)
tan co-function identity
cot(pi/2 - t)
cot co-function identity
tan(pi/2 - t)
Is secant an even or odd function
even
Is Cosecant an even or odd function
odd
what are the periods of sec and csc
2kpi
reciprocal identity of csc(t)
1/sin(t)
reciprocal identity of sec(t)
1/cos(t)
reciprocal identity of cot(t)
1/tan(t)
reciprocal identity of sin(t)
1/csc(t)
reciprocal identity of cos(t)
1/sec(t)
reciprocal identity of tan(t)
1/cot(t)
quotient identity of tan(t)
sin(t)/cos(t)
tangent is positive in which quadrants
1 and 3
sine is positive in which quadrants
1 and 2
cosine is positive in which quadrants
1 and 4
amplitude for sine and cosine
distance between top and bottom of wave divided by 2
phase shift for sine and cosine
location of the peak closest to the x axis
baseline
the mid-point of the wave
formula for the period of sine and cosine
2pi / omega (ω)
formula for phase shift
- phi (φ) / omega (ω)
What is the amplitude of the following:
3 sin (4t + pi/3) + 5
3
What is the baseline of the following:
3 sin (4t + pi/3) + 5
5
What is the phase of the following:
3 sin (4t + pi/3) + 5
pi/3
What is the period of the following:
3 sin (4t + pi/3) + 5
2pi/4
What is the phase shift of the following:
3 sin (4t + pi/3) + 5
- (pi/3) / 4
What is the formula for the period of Tangent
pi / omega (ω)
How do you find the amplitude of Tangent
period / 4
How do you find the asymptote of Tangent
period / 2
Transformations formula for cosine
f(t) = a cos (ωt + φ) + b
Where is the phase shift of Cotangent
The Asymptote
How do you find the amplitude of Cotangent
period / 4
Where is the period of cotangent
From asymptote to asymptote
formula to find Tangent
y/x or sin/cos
formula to find Cotangent
x/y or cos/sin
cosine addition formula
cos(s + t) = cos(s) * cos(t) - sin(s) * sin(t)
sine addition formula
sin(s + t) = cos(s) * sin(t) + sin(s) * cos(t)
tangent addition formula (without simplification)
tan(s + t) = sin(s + t) / cos(s + t)
tangent addition formula (simplified)
tan(t) + tan(s) / 1 - tan(t) * tan(s)
cosine subtraction formula
cos(s - t) = cos(s) * cos(t) + sin(s) * sin(t)
sine subtraction formula
sin(s - t) = sin(s) * cos(t) − cos(s) * sin(t)
cosine double-angle formula
cos(2t) = cos^2(t) - sin^2(t)
sine double-angle formula
sin(2t) = 2cos(t)sin(t)
tangent subtraction formula
tan(α−β)= tan(α)−tan(β) / 1+tan(α)tan(β)
tangent double-angle formula
tan(2t) = 2tan(t) / 1 - tan^2(t)
