Algebra 2/Trigonometry Regents Review – Flashcards
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When raising a negative number to a power always put the negative number in a parenthesis.
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Raising a negative number to a power
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If both terms are opposite signs they can be crossed out and replaced by a negative 1.
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Canceling out opposites
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To factor out a -1, remove the negative and change the signs of the terms
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Factoring out a -1
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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.
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Equations with fractions
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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.
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Quadratic formula (Find the Roots)
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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
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Discriminant (describe the roots)
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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.
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Sum and product of roots
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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 (?) 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.
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Absolute value inequalities
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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.
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Absolute value equations
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The inverse variation formula is x one times x two equals y one times y two. Inverse variation creates a corner hyperbola.
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Inverse variation
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To find the conjugate The first term stays the same. Change the sign of the second term.
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Conjugate
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The domain is the x coordinates. The range is the y coordinates. To find the inverse switch the x and y coordinates.
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Domain, range, inverse
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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.
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Function
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A one to one function must pass the vertical and horizontal line test. No x or y coordinate can repeat.
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One to one function
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To convert from degrees to radians multiply the degrees by pi and divide by 180.
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Convert degrees to radians
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To convert from radians to degrees, multiply the radians by 180 and divide by pi.
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Convert radians to degrees
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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.
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Degrees and radians
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In a circle the central angle in radians equals the arc length divided by radius.
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Arc length - radius formula
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The circle formula is x minus h squared plus y minus k squared equals the radius squared.
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Circle formula
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Secant equals 1 divided by cosine.
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Secant
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Cosecant equals 1 divided by sine.
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Cosecant
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cotangent equals 1 divided by tangent or cosine divided by sine.
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Cotangent
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Tangent equals sine divided by cosine.
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Tangent
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Cosine squared plus sine squared equals 1.
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Trigonometric identity
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An arithmetic sequence is created by adding or subtracting a common difference.
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Arithmetic sequence
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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.
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Geometric sequence
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a to the n minus 1 - look to the term behind. a to the n plus 1 - loot to the term in front.
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Recursive sequences
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To rationalize a denominator multiply the numerator (top) and denominator (bottom) by the conjugate of the denominator (bottom).
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Rationalizing the denominator
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Survey - ask Observation study - watch Experiment - change
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Survey, observational study, experiment
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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.
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Quadrants
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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.
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Converting radians to degrees and minutes
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Coterminal angles are just different ways of naming the same angle.
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Conterminal Angles
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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.
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Area of a triangle (need S.A.S.)
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A parallelogram is made up of 2 congruent triangles.
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Area of a parallelogram
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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.
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Law of Sines
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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.
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Law of cosines given (S.A.S.)
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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.
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Law of cosines given (S.S.S.)
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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.
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Vector problems
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To solve square root equations Isolate the square root on one side of the equation. Square both sides of the equation Check the answer(s) in the original equation for extraneous roots.
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Square root equations
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To convert from logarithmic form to exponent form the base remains the base and the rest of the stuff crosses. the b and the n can never be negative.
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Converting between logarithm and exponent form
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Inverses of exponential and logarithmic equations
