Pre-calc

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Pre Cal

luonut neel patel

HARDWARE AND SOFTWARE

luonut I. Orokieta

Derivatives

luonut Steve Kangas

Trigonometry with The Unit Circle Cited and Colored

luonut Widad Karsou

Pre-calc

Trig Functions

Cotangent= adjacent/ opposite or x/y

Secant= hypotenuse/ adjacent or 1/x

Cosecant= hypotenuse/ opposite or 1/y

Tangent=opposite/adjacent or y/x

Cosine= Adjacent/hypotenuse or x/1

Sine= opposite/hypotenuse or y/1

S.O.H C.A.H T.O.A Fun way to remember it Some old hippie Caught another hippie Tripping on acid

Fundamentals of trig identities

Standard Trig Identities sin(Theta)=y cos(theta)=x tan(theta)=y/x

Reciprocal Identities csc(theta)=1/y=1/sin(theta0 sec(theta)=1/x=1/cos(theta) cot(theta)=x/y=1/tan(theta)

Quotient Identities tan(theta)=y/x=sin(theta)/cos(theta) cot(theta)=x/y=cos(theta)/sin(theta)

For an angle Theta in standard position, let P=(x,y) be the point on the terminal side of Theta that is also on the circle x^2+y^2=1, the unit circle.

Formulas for triangles

Quadrant I All are positive Quadrant II sin and cosecant are positive cosine, tangent, secant and cotangent are negative Quadrant III sine, cosine, cosecant and secant are negative tangent and cotangent are positive Quadrant IV sine, tangent, cosecant and cotangent are negative cosine and secant are positive

Solving for trigonometric equations example: solve the equation: sin(2theta)=1/2, 0

Solutions for cos reflect across the x-axis solutions for sin reflect across y-axis solutions for tan reflect across the diagonal y=x

Law of Cosines

In trig, the Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles using the equations above.

a^2=b^2+c^2-2bc*cos(A) b^2=a^2+c^2-2ac*cos(B) c^2=a^2+b^2-2ab*cos(C)

Law of Sines

The Law of Sines is very useful for solving triangles: a /sin A=b/sin B=c/sin C a, b and c are sides. A, B and C are angles. The sides and angles correspond meaning side a faces angle A, side b faces angle B and side c faces angle C.