110_1_TRIGONOMETRY

# 110_1_TRIGONOMETRY - TRIGONOMETRY Angles Arc length...

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TRIGONOMETRY

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Angles, Arc length, Conversions Angle measured in standard position. Initial side is the positive x ! axis which is fixed. Terminal side is the ray in quadrant II, which is free to rotate about the origin. Counterclockwise rotation is positive, clockwise rotation is negative. Coterminal Angles: Angles that have the same terminal side. 60 ! , 420 ! , and ! 300 ! are all coterminal. Degrees to radians: Multiply angle by . 180 ! ! 3 180 60 ! ! " # ! ! radians Radians to degrees: Multiply angle by . 180 ! ! ! ! 45 180 4 " # ! ! Arc length = central angle x radius, or . r s \$ " Note: The central angle must be in radian measure. Note: 1 revolution = 360 ! " \$% &’()’*+,
Right Triangle Trig Definitions - sin(A) = sine of A = opposite / hypotenuse = a/c - cos(A) = cosine of A = adjacent / hypotenuse = b/c - tan(A) = tangent of A = opposite / adjacent = a/b - csc(A) = cosecant of A = hypotenuse / opposite = c/a - sec(A) = secant of A = hypotenuse / adjacent = c/b - cot(A) = cotangent of A = adjacent / opposite = b/a A a b c B C

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Special Right Triangles 30 ! 45 ! 60 ! 45 ! 2 1 3 1 1 2 3 3 ) 30 tan( 2 1 ) 30 sin( 2 3 ) 30 cos( " " " ! ! ! 3 ) 60 tan( 2 3 ) 60 sin( 2 1 ) 60 cos( " " " !
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