Section 1
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Arithmetic sequence
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Cards (56)
Section 1
(50 cards)
Arithmetic sequence
An arithmetic sequence is created by adding or subtracting a common difference.
Arc functions
Converting radians to degrees and minutes
Multiply by 180 and then divide by pi. The part before the decimal is the degrees. Multiply the decimal by 60 to find the minutes.
Inverse variation
The inverse variation formula is x one times x two equals y one times y two. Inverse variation creates a corner hyperbola.
Conterminal Angles
Coterminal angles are just different ways of naming the same angle.
Cosecant
Cosecant equals 1 divided by sine.
Secant
Secant equals 1 divided by cosine.
Complex fractions
Equations with fractions
To solve equations with fraction, find a common denominator. Drop the denominators Solve the resulting equation. Check the answer(s) in the denominators for extraneous roots.
Law of Sines
The law of sines is a divided by sine of A equals b divided by sine of B equals c divided by sine of C.
Trigonometric identity
Cosine squared plus sine squared equals 1.
Absolute value inequalities
To solve absolute value inequalities Isolate the absolute value on one side of the equation. Change the inequality sign and the sign(s) of the terms on the right to the opposite signs. If the original inequality has a greater than or greater than or equal to (≥ or >) sign use or between your solutions. Solution is <(≤) x or x >(≥) solution. If the original inequality has a less than or less than or equal to (≤ or <) write as an interval. Solution <(≤) x <(≤) solution. You have to divide by a negative, do not forget to flip the inequality sign.
Binomial Expansion
Arc length - radius formula
In a circle the central angle in radians equals the arc length divided by radius.
Function
To be a function It must pass the vertical line test. No x coordinate can repeat. An equation must have a y, but the y cannot be squared.
Quadratic formula (Find the Roots)
the quadratic formula is x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a.
Geometric sequence
A geometric sequence is created by multiplying or dividing a common ratio. If the terms alternate between positive and negative, the common ratio is negative.
Absolute value equations
To solve an absolute value equation Isolate the absolute value on one side of the equation. Change the sign(s) of the terms on the right to the opposite sign(s). check your answer(s) for extraneous roots.
Factoring by grouping
Law of cosines given (S.S.S.)
The law of cosines a squared(the side across from the angle) equals b squared plus c squared minus 2 times b times c times the cosine of x (A). Use numerical solve to find the measure of angle A.
Law of cosines given (S.A.S.)
The law of cosines is b squared plus c squared minus 2 times b times c times the cosine of A. Take the square root of the answer to find the missing side.
Sum and product of roots
The sum of the roots is negative b divided by a. The product of the roots is c divided by a. The equation for sum and product of the roots is x squared minus the sum times x plus the product equals 0.
Area of a triangle (need S.A.S.)
Need side angle side (S.A.S) to find area. The area of a triangle equals ½ times a times b times sine of C.
Factoring out a -1
To factor out a -1, remove the negative and change the signs of the terms
Discriminant (describe the roots)
if the discriminant is 0, the roots are real, rational and equal. if the discriminant is negative, the roots are complex or imaginary. if the discriminant is a perfect square, the roots are real, rational, and unequal. if the discriminant is not a perfect square, the roots are real, irrational, and unequal
Quadrants
All students take classes. Sine and cosecant are positive in quadrants 1 and 2. Cosine and secant are positive in quadrants 1 and 4. Tangent and cotangent are positive in quadrants 1 and 3.
Completing the square
Conjugate
To find the conjugate The first term stays the same. Change the sign of the second term.
Permutations with repetition
Circle formula
The circle formula is x minus h squared plus y minus k squared equals the radius squared.
Tangent
Tangent equals sine divided by cosine.
Canceling out opposites
If both terms are opposite signs they can be crossed out and replaced by a negative 1.
Rationalizing the denominator
To rationalize a denominator multiply the numerator (top) and denominator (bottom) by the conjugate of the denominator (bottom).
Raising a negative number to a power
When raising a negative number to a power always put the negative number in a parenthesis.
Operations with fractions
Convert radians to degrees
To convert from radians to degrees, multiply the radians by 180 and divide by pi.
Degrees and radians
Once around a circle is 2 pi radians or 360 degrees. ½ of the way around a circle is pi radians or 180 degrees. ¼ of the way around a circle is pi divided by 2 or 90 degrees.
Ambiguous Case (0,1,2 triangles?
Sine, Cosine, Tangent on the unit circle
Area of a parallelogram
A parallelogram is made up of 2 congruent triangles.
One to one function
A one to one function must pass the vertical and horizontal line test. No x or y coordinate can repeat.
Recursive sequences
a to the n minus 1 - look to the term behind. a to the n plus 1 - loot to the term in front.
Domain, range, inverse
The domain is the x coordinates. The range is the y coordinates. To find the inverse switch the x and y coordinates.
Logarithms
Convert degrees to radians
To convert from degrees to radians multiply the degrees by pi and divide by 180.
Cotangent
cotangent equals 1 divided by tangent or cosine divided by sine.
Factoring ax²+bx+c
Exact values of trigonometric functions
Survey, observational study, experiment
Survey - ask Observation study - watch Experiment - change
Vector problems
To solve vector problems remember that The opposite sides in a parallelogram are congruent. The consecutive angles in a parallelogram are supplemental (add up to 180 degrees). Use law of Cosines to find the resultant and the angle between the 2 forces. Use law of Sines to find the angle between a force and the resultant.
Section 2
(6 cards)