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67 Cards in this Set
- Front
- Back
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The inverse sine function |
Y=sin-1x where x is greater than or equal to -1, and less than or equal to 1. Y is also greater than or equal to -pi/2 and less than or equal to pi/2 |
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The inverse cosine function |
Y=cos-1x where x is greater than or equal to -1 and less than or equal to 1. Y is also greater than or equal to 0 and less than or equal to pi |
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The inverse tangent |
Y=tan-1x where x is a real number and y is greater than -pi/2 and less than pi/2. It also has horizontal asymptotes at -pi/2 and pi/2 |
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The inverse secant function |
Where the absolute value of x is greater than or equal to 1 and 0 is less than or equal to y which is less than pi/2. OR pi/2 is less than y which is less than or equal to pi |
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The inverse cosecant function |
Where the absolute value of x is greater than or equal to 1 and -pi/2 is less than or equal to y which is less than 0. OR 0 is less than y which is less than or equal to pi/2 |
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The inverse cotangent function |
Where x is any real number and 0 is less than y which is less than pi |
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Identity |
Equation that is true for all values of x for which the expressions on the left and right are defined |
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Conditional equation |
Equation that is true only for some values of the variable |
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Reciprocal rule for sin and cos |
1/csc and 1/sec |
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Reciprocal rule for tan and csc |
1/cot and 1/sin |
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Reciprocal rule for sec and cot |
1/cos and 1/tan |
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Pythagorean identity 1 |
Sin squared + cos squared = 1 |
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Pythagorean identity 2 |
1 + tan squared = sec squared |
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Pythagorean identity 3 |
1 + cot squared = csc squared |
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Quotient identity of tan |
Sin/cos |
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Quotient identity of cot |
Cos/sin |
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The odd functions |
Sin, tan, csc, cot |
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The even functions |
Cos and sec |
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Log quotient |
Log a (x/y) = log a (x) - log a (y) |
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Log power |
Log a (x squared) = 2log a (x) |
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Log product |
Log a (xy) = log a (x) + log a (y) |
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Sin and cos cofunction identities |
Sin x = cos((pi/2)-x) cos x = sin((pi/2)-x) |
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Tan and cot cofunction identities |
Tan x = cot((pi/2)-x) cot x = tan((pi/2)-x) |
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Sec and csc cofunction identities |
Sec x = csc((pi/2)-x) csc x = sec((pi/2)-x) |
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Sin and cos periodic identities |
Sin(x+2pi)=sinx Cos(x+2pi)=cosx |
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Tan and cot periodic identities |
Tan(x+pi)=tanx Cot(x+pi)=cotx |
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Csc and sec periodic identities |
Csc(x+2pi)=cscx Sec(x+2pi)=secx |
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Sum of A sin x and B cos x |
A sin x + B cos x = k sin(x+a) where k= the square root of a squared + b squared and a satisfied cos a = a/k and sin a = b/k |
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Sin2x |
2sinxcosx |
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Tan2x |
2tanx/1-tan squared x |
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Cos2x |
Cos squared x - sin squared x 1-2sin squared x 2cos squared x -1 |
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Power reducing formula sin squared x |
1-cos2x/2 |
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Power reducing formula cos squared x |
1+cos2x/2 |
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Power reducing formula tan squared x |
1-cos2x/1+cos2x |
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Half angle formulas |
The + or - is determined by the quadrant in which the angle a/2 lies |
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Where does sinx = 0 |
0 and pi |
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Where does cos = 1 |
0 |
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Where does sinx = 1/2 |
Pi/6 and 5pi/6 |
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Where cosx = (square root of 3)/2 |
Pi/6 and 11pi/6 |
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Where does sinx = (square root of 2)/2 |
Pi/4 and 3pi/4 |
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Where does cosx = (square root of 2)/2 |
Pi/4 and 7pi/4 |
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Where does sinx = (square root of 3)/2 |
Pi/3 and 2pi/3 |
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Where does cosx = 1/2 |
Pi/3 and 5pi/3 |
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Where does sinx = 1 |
Pi/2 |
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Where does cosx = 0 |
Pi/2 and 3pi/2 |
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Where does sinx = -1/2 |
7pi/6 and 11pi/6 |
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Where does cosx = -1/2 |
2pi/3 and 4pi/3 |
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Where does sinx = -(square root of 2)/2 |
5pi/4 and 7pi/4 |
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Where does cosx = -(square root of 2)/2 |
3pi/4 and 5pi/4 |
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Where does sinx = -(square root of 3)/2 |
4pi/3 and 5pi/3 |
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Where does cosx = -(square root of 3)/2 |
5pi/6 and 7pi/6 |
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Where does sinx = -1 |
3pi/2 |
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Where does cosx = -1 |
Pi |
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Where does tanx = 0 |
0 and pi |
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Where is cotx undefined |
0 and pi |
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Where does tanx = (square root of 3)/3 |
Pi/6 and 7pi/6 |
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Where does cotx = square root of 3 |
Pi/6 and 7pi/6 |
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Where do cotx and tanx equal 1 |
Pi/4 and 5pi/4 |
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Where does tanx = square root of 3 |
Pi/3 and 4pi/3 |
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Where cotx = (square root of 3)/3 |
Pi/3 and 4pi/3 |
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Where is tanx undefined |
Pi/2 and 3pi/2 |
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Where does cotx = 0 |
Pi/2 and 3pi/2 |
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Where does tanx = -(square root of 3) |
2pi/3 and 5pi/3 |
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Where does cotx = -(square root of 3)/3 |
2pi/3 and 5pi/3 |
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Where do cotx and tanx = -1 |
3pi/4 and 7pi/4 |
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Where does tanx = -(square root of 3)/3 |
5pi/6 and 11pi/6 |
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Where does cotx = -(square root of 3) |
5pi/6 and 11pi/6 |
