special angles and trig equations and identities
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Sin 0 | 0
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| Cos 0 | 1
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| Tan 0 | 0
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| Sin pi/6 | 1/2
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| Cos pi/4 | Square root of 2/2
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| Tan pi/6 | Square root of 3/3
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| Cos pi/6 | Square root of 3/2
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| Sin pi/4 | Square root of 2/2
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| Tan pi/4 | 1
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| Sin pi/3 | Square root of 3/2
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| Cos pi/3 | 1/2
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| Tan pi/3 | Square root 3
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| Sin pi/2 | 1
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| Cos pi/2 | 0
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| Tan pi/2 | Undefined
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| Sum formula for Sin | SinACosB+CosASinB
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| Sum formula for Cos | CosACosB-sinAsinB
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| Sum formula for Tan | tanA+tanB/1-tanAtanB
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| Difference Formula for sin | sin(A-B)= sinAcosB-cosAsinB
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| Double angle formula for sin | sin(2A)= 2sinAcosA
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| half-angle formula for sin | sin(A/2)= (+-)Square root of (1-cosA/2)
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| tanA | sinA/cosA
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| cotA | cosA/sinA
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| Pythagorean identity 1 | sin^2(A) + cos^2(A) = 1
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| Law of sines | a/sinA = b/sinB = c/sinC
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| Law of cosine | a^2 = b^2 + c^2 - 2bc cosA
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| Parabola: formulas | Formulas: y^2 = 4px when parabola on x-axis
x^2 = 4py when parabola on y-axis
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| Ellipse: formula | formula: (x^2/a^2) + (y^2/b^2) = 1
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| Hyperbola: formulas | Formulas: (x^2/a^2) - (y^2/b^2) = 1
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| double angle formula for cos | cos(2A)= cos^2(A)-sin^2(A)
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| double angle formula for tan | tan(2A)= 2tanA/1-tanA
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| Difference Formulas for cos | cos(A-B)= cosAcosB+sinAsinB
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| Difference Formulas for tan | tan(A-B)= tanA-tanB/1+tanAtanB
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| half-angle formula for cos | cos(A/2)= square root of (1+cosA/2)
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| half-angle formula for tan | tan(A/2)= square root of (1-cosA/1+cosA)
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| Pythagorean identity 2 | tan^2(A) + 1 = sec^2(A)
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| Pythagorean identity 3 | 1 + cot^2(A)= csc^2(A)
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| Parabola: Foci | for when on x-axis (p,0) for when on y-axis (0,p)
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| Ellipse: Foci | when a is bigger ((+-) square root of (a^2 - b^2), 0)
when b is bigger (0, (+-) square root of (b^2 - a^2))
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| Hyperbola: Foci | When on x-axis, ((+-) square root of (a^2 + b^2), 0)
When on y-axis, (0, (+-)square root of (b^2+a^2))
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| y = f(x) + c | Vertical shift c units up
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| y = f(x) - c | Vertical shift c units down
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| y = f(x + c) | Horizontal shift c units to the left
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| y = f(x - c) | Horizontal shift c units to the right
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| y = -f(x) | Reflection over x-axis
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| y = f(-x) | Reflection over y-axis
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| y = cf(x) | vertical stretch/shrink, when c > 1 it's stretch, (x,y)--> (x,y*c)
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| y = f(cx) | horizontal stretch/shrink, c < 1 it's shrink, (x,y)--> (x*(1/c),y)
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| a^0 = | 1
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| a^-n = | 1/a^n
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| a^m(a^n) = | a^(m+n)
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| a^m/a^n = | a^(m-n)
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| (a^m)^n = | a^m*n
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| (ab)^n = | (a^n)b^n
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| log base a of 1 = | 0
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| log base a of a = | 1
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| log base a of a^n = | n
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| a^log base a of x = | x
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| log base a of (UV) = | log base a of U + log base a of V
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| log base a of (u/v) = | log base a of u - log base a of v
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| log base a of u^n = | n*log base a of U
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| log base a of U = | log base b of U/ log base b of a
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Created by:
burtond
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