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Trigonometry

Trigonometry

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Pre ? Calculus Math 40S: Explained! www.math40s.com 9 Pre ? Calculus Math 40S: Explained! www.math40s.com 10 Trigonometry Lesson 2 Part One ? The Unit Circle The Unit Circle What you see here is the unit circle. This is a useful tool in: a) Comparing angles in degrees & radians. b) Finding exact values of the six trigonometric ratios. It is very important you memorize the unit circle

Algebra Sin, Cos, and Tan

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A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question. In any right angled triangle, for any angle: The sine of the angle = the length of the opposite side the length of the hypotenuse The cosine of the angle = the length of the adjacent side the length of the hypotenuse The tangent of the angle = the length of the opposite side the length of the adjacent side So in shorthand notation:

Sin Cos and Tan

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In a right triangle where theta is given and a side is given you can solve for anything. To solve for the hypotenuse use the phrase SOH CAH TOA. If the angle and the opposite are given use opposite side divided by sin of the angle. and vice versa for all other sides and angles. Soh cah toa stands for Sin opposite over Hypotenuse Cosin adjacent over hypotenuse Toa opposite over adjacent all of these are with respect to theta.

Derivations of Trigonometry Formulas

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Given: sin(a+ b) = sin a cos b+ cos a sin b, we can figure out the following: sin(a? b) = sin(a+ (?b)) = sin a cos(?b) + cos a sin(?b) = sin a cos b+ cos a(? sin b) = sin a cos b? cos a sin b cos(a+b) = sin (pi 2 ? (a+ b) ) = sin ((pi 2 ? a ) ? b ) = sin (pi 2 ? a ) cos b?cos (pi 2 ? a ) sin b = cos a cos b?sin a sin b cos(a? b) = cos(a+ (?b)) = cos a cos(?b)? sin a sin(?b) = cos a cos b? sin a(? sin b) = cos a cos b+ sin a sin b tan(a+ b) = sin(a+ b) cos(a+ b) = sin a cos b+ cos a sin b cos a cos b? sin a sin b ? sec a sec b sec a sec b = sin a sec a+ sin b sec b 1? sin a sec a sin b sec b = tan a+ tan b 1? tan a tan b tan(a? b) = tan(a+ (?b)) = tan a+ tan(?b) 1? tan a tan(?b) = tan a+ (? tan b) 1? (? tan a tan b) = tan a? tan b 1 + tan a tan b

Trig Identities

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Pine Crest School Pre-Calculus Honors Handy Dandy Trigonometric Identities Reference Sheet RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES sin2 x + cos2 x = 1 1 + cot2 x = csc2 x tan2 x + 1 = sec2 x SYMMETRY IDENTITIES cos (?x) = cos x sin (?x) = ? sin x tan (?x) = ? tan x CO-FUNCTION IDENTITIES = sin x = csc x = tan x ANGLE SUM IDENTITIES sin(x + y) = sin x cos y + cos x sin y sin(x ? y) = sin x cos y ? cos x sin y cos(x+y) = cos x cos y ? sin x sin y cos(x ? y) = cos x cos y + sin x sin y DOUBLE ANGLE IDENTITIES sin 2x = 2 sin x cos x cos 2x = cos2x ? sin2x = 2 cos2x ? 1 = 1 ? 2 sin2x HALF ANGLE IDENTITIES

Trigonometry Reference Chart

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Trigonometry sin cos circle Trig
The unit circle is a commonly used tool in trigonometry because it helps the user to remember the special angles and their trigonometric functions. The unit circle is a circle drawn with its center at the origin of a graph(0,0), and with a radius of 1. All angles are measured starting from the x-axis in quadrant one and may go around the unit circle any number of degrees. Points on the outside of the circle that are in line with the terminal (ending) sides of the angles are very useful to know, as they give the trigonometric function of the angle through their coordinants. The format is (cos, sin). Note that in trigonometry, an angle can be of any size, positive or negative. An angle larger than 360º means that you have gone round the circle more than once.

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