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| Triangles Inscribed in Circles |
The measure of an angle inscribed in a circle is half the intercepted arc. This means that an angle inscribed in a half circle is 90 degrees. <B = 90 |
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| Inverse Functions |
If the g(f(x)) = x, then f(x) and g(x) are inverse functions of each other, and if you have f(x) = 3x + 1, change it to y=3x+1, switch the x and y and solve for y, which gives you g(x) |
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| Logs |
Given an equation such as:
First set it equal to x, and then take it out of logs:
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| Arcsin and Arccos |
Arcsin, arccos and arctan are a different way of saying "Inverse sin", "inverse cos" or "inverse tan". |
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| Synthetic Division |
If you are dividing an equation by x + 2, reverse the sign on the 2 to make it -2. And remember to check to make sure every power of x is included. If there is no x squared term, then call it 0x^2. |
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| Mins and Maxes in Parabolas |
The min or max of a parabola is the y value of the vertex. |
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| Equations of Circles |
(x - h)^2 + (y - k)^2 = radius ^squared
where h, k is the center. |
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| Quadratic Roots |
The roots of a quadratic equation means, how many times does the parabola cross the x-axis.
In this image, the yellow parabola has NO real roots, the red one has ONE real root and the blue one has TWO real roots.
Using ax^2 + bx + c = 0, to determine how many roots a quadratic equation has, use the discriminant, which is part of the quadratic formula:
b^2 - 4ac
If b^2 - 4ac < 0, there are NO real roots
If b^2 - 4ac = 0, there is ONE real root
If b^2 - 4ac > 0, there are two real roots |
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| If then statements |
In an if then statement, such as if A then B. The only other statement which is always true is the contrapositive, which says if NOT B then NOT A. |
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| Factorials |
6! means 6x5x4x3x2x1. This function can be found on the TI-82 and TI_83, click the math button, scroll over to PRB with the right arrow, and the factorial button is in the list of functions. |
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| Dividing by a fraction |
Multiply by the reciprocal. 5 divided by 2/3 means 5 x 3/2, or 15/2. |
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| Even and Odd Functions |
Even functions are symmetry with respect to the y axis, as y=x^2 is. Y = cos(x) is an even function.
Odd functions are symmetric with respect to the origin. Y = x^3 and y =
sin(x) are odd. |
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| Distance Formula On Three Dimensional Graph |
In three dimensional graphs, points have three values: x, y and z.
The distance formula is similar to the formula on an x,y coordinate graph.
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| Mins and Maxes |
Minimums and maximums on a graph are always the Y value |
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| Polar Graphing |
Points on a graph can be found by one of two ways. If you have an x and y value, you can get to a point using these.
A second way to get to a point is thinking about the radius of a circle, with the point being the end of the radius, and then knowing that it forms an angle of a certain size with the X axis.
To find the x and y values of this point:
x = r sin(Θ)
y = r cos(Θ) |
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| Trig Identity |
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| Translations |
When a number is added or subtracted inside the parentheses, then it is a horizontal shift in the opposite direction, so for x - 2, the graph is shifted 2 to the right. When the number is outside of what is being done to x, such as "+ 3" here, it is a vertical shift in the same direction, so up 3.
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| Equations of lines |
Point-slope formula, where (x1, y1) is a point on the graph and m is the slope.
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Slope-intercept formula, where m is the slope and b is the y-intercept.
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Standard form, a pretty useless form of an equation of a line, you have to solve for y to the the slope-intercept form.
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