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trigonometry

chapter 9/10 - trigonometry

TermDefinition
the cosine rule of a triangle a^2 = b^2 + c^2 - 2b*c*cos(A)
the sine rule of length for a triangle a/sin(A) = b/sin(B) = c/sin(C)
the sine rule of area for a triangle area = 0.5*a*b*sin(C)
angles and the sine rule sin(180-theta) = sin(theta) so context on if an angle is acute, obtuse or if it can be both is needed
f(x) = sin(x) a periodic function, period 360 degrees has a maximum/minimum of 1/-1 respectively
f(x) = cos(x) identical to sin(x+90 degrees) a periodic function, period 360 degrees has a maximum/minimum of 1/-1 respectively
f(x) = tan(x) a periodic function, period 180 degrees range is the real numbers is undefined for x = 90 + n*180 degrees, where n is an integer
af(bx+c) + d in the case of trigonometry a periodic function, period (base period/b) has a maximum/minimum of (base max/min * a)+d
trigonometry of the unit circle a point of the circle P(x,y) = (cos(theta),sin(theta)) the gradient of the line OP = y/x = tan(theta) theta is the anticlockwise angle of the positive x-axis to OP
negatives and trigonometric functions sin(-theta) = -sin(theta) cos(-theta) = cos(theta) tan(-theta) = -tan(theta) these, and more, can be memorised using a CAST diagram
trigonometric identities sin^2(x) + cos^2(x) = 1 tan(x) = sin(x)/cos(x)
the principal value of trigonometric functions since the “inverse” of the trig functions aren’t true inverses, their output is within a given range: 0 <= arcsin(x) <= 180 degrees -90 <= arccos(x) and arctan(x) <= 90 degrees
f(ax+b) trigonometric equations consider the given domain of f(x) and how ax+b changes it, then solve the equation and consider all the possible solutions
quadratic equations in terms of quadratic functions ensure that the equation is in terms of only 1 trigonometric function, then factorise/solve as normal, ensuring erroneous/extra roots are accounted for
Created by: That cool NAMe
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