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Midterm_2_reference_sheet[1]

# Midterm_2_reference_sheet[1] - Math 4C Fall 2007 Midterm 2...

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Math 4C Fall 2007 Midterm 2 Reference Sheet Trigonometric functions Of acute angles sin " = opp hyp , cos " = adj hyp , tan " = opp adj Of any angle sin " = y r , cos " = x r , tan " = y x ( x # 0) (circle radius r ) Of real numbers sin t = y , cos t = x , tan t = y x ( x " 0) Radians and degrees 180 °= " (radians) Solving general triangles Law of Sines sin A a = sin B b = sin C c Law of Cosines a 2 = b 2 + c 2 " 2 bc cos A , cos A = ( b 2 + c 2 " a 2 ) /(2 bc ) Area of a triangle A = 1 2 ab sin " , A = 1 4 ( a + b + c )( a + b # c )( a + c # b )( b + c # a ) Unit Circle Translations, reflections, and dilations y = A sin[ B ( x " C )] + D , y = A cos[ B ( x " C )] + D Horizontal translation (phase shift) C units Vertical translation (vertical shift) D units Horizontal dilation By factor of 1 B (period becomes 2 " B ) Vertical dilation (amplitude) By factor of A Reflections " f ( x ) reflect across x -axis; f ( " x ) across y -axis

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