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Level 424

Trigonometry II


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Sum and Difference Formulas
sinA * cosB + cosA * sinB
Sum and Difference Formulas
sinA * cosB - cosA * sinB
Sum and Difference Formulas
cosA * cosB - sinA * sinB
Sum and Difference Formulas
cosA * cosB + sinA * sinB
Sum and Difference Formulas
(tanA + tanB) / (1 - tanA * tanB)
Sum and Difference Formulas
(tanA - tanB) / (1 + tanA * tanB)
sinθ = ?
y / r
cosθ = ?
x / r
tanθ = ?
y / x
cotθ = ?
x / y
secθ = ?
r / x
cscθ = ?
r / y
sinθ / cosθ
Ratio identity tanθ = ?
cosθ / sinθ
Ratio identity cotθ = ?
Pythagorean identity of cosθ?
cosθ = ± √1 - sin^2θ
Pythagorean identity of sinθ?
sinθ = ± √1 - cos^2θ
sinθ = 0
Exact values for θ = 0°
sinθ = 1 / 2
Exact values for θ = 30°
sinθ = √2 / 2
Exact values for θ = 45°
sinθ = √3 / 2
Exact values for θ = 60°
sinθ = 1
Exact values for θ = 90°
θ × π/180
Convert degrees to radians
θ × 180/π
Convert radians to degrees
Find a coterminal angle (clockwise)
θ - 360° or θ - 2π
Find a coterminal angle (counterclockwise)
θ + 360° or θ + 2π
Pythagorean Theorem
in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
(0,0), (π/2,1), (π,0), (3π/2,-1), (2π,0)
What are the 5 critical points for sine?
(0,1), (π/2,0), (π,-1), (3π/2,0), (2π,1)
What are the 5 critical points for cosine?
A = amplitude
In y = A sin B (x-H) + K, what do A, B, H and K represent?
Frequency?
1 / period
Inverse Functions?
Switch x and y. Ex:
Even Function
graph is symmetrical with respect to the y-axis; f(x) = f(-x)
Odd Function
graph is symmetrical with respect to both the x-axis and y-axis; f(-x)=-f(x)
Trigonometric Identity
An equation containing a trigonometric function that any angle will solve.
sin(A ± B)
sinAcosB ± sinBcosA
cos(A ± B)
cosAcosB -+ sinAsinB
Sec^2(x)
tan^2(x) + 1
cosec^2(x)
cot^2(x) + 1
sin2x
2sinxcosx
cos2x
cos^2(x) - sin^2(x)
tan2x
(2tan(x))/(1 - tan^2(x))
sin(x) in terms of cos(x)
sin(x) = cos(x - 90)
cos(x) in terms of sin(x)
cos(x) = sin(x + 90)
Cosine rule
a^2 = b^2 + c^2 - 2bc cosA
½absinC
Area of a triangle
* 2π/360
Deg. -> Rad.
* 360/2π
Rad. -> Deg.
tan(A + B)
(tanA + tanB)/1 - tanAtanB
b/sinB = c/sinC
For all triangles, a/sinA =
sin(-x)
-sin x
cos(-x)
cos x
tan(-x)
-tan x
tan x
sin x / cos x
cot x
cos x/ sin x
1/sin x
csc x
1/cos x
sec x
cot x
1/ tan x
y/r
sin θ
x/r
cos θ
y/x
tan θ
r/y
csc θ
r/x
sec θ
x/y
cot θ
opp/hyp
sin θ
adj/hyp
cos θ
opp/adj
tan θ
hyp/opp
csc θ
hyp/adj
sec θ
adj/opp
cot θ
√2/2
sin 45°
√2/2
cos 45°
1
tan 45°
1/2
sin 30°
√3/2
cos 30°
√3/3
tan 30°
√3/2
sin 60°
1/2
cos 60°
√3
tan 60°
1
sin^2 x + cos^2 x
csc^2 x
1+ cot^2 x
1+tan^2 x
sec^2 x
sin(90-x)
cos x
cos(90-x)
sin x
tan(90-x)
cot x
sin(u±v)
(sin u)(cos v) ±(cos u)(sin v)
cos(u±v)
(cos u)(cos v)∓(sin u)(sin v)
tan(u±v)
tan u±tan v/1∓(tan u)(tan v)
sin(π/2-x)
cos x
tan(π/2-x)
cot x
sec(π/2-x)
csc x
cos(π/2-x)
sin x
cot(π/2-x)
tan x
csc(π/2-x)
sec x
sin(x+π/2)
cos x
cos(x+π/2)
-sin x
sin 2x
2 sin x cos x
cos 2x
cos^2 x - sin^2 x
1-2*sin^2 x
cos 2x
cos 2x
2 cos^2 x -1
±√1-cos x/2
sin x/2
Cos x/2
±√1+cos x/ 2
Tan x/2
±√1-cos x/ 1+cos x