Trigonometric

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Trigonometric

Trigonometric Equations and Trigonometric Identities

- Quotient Identities tan pi= sin pi/cos pi cot pi= cos pi/sin pi - Reciprocal Identities csc pi=1/sin pi sec pi=1/cos pi cot pi=1/tan pi - Pythagorean Identities sin2pi+cos2pi=1 tan2pi+1=sec2pi cot2pi+1=csc2pi -Even-Odd Identities sin(-pi)= - sin pi cos(-pi)=cos pi tan(-pi)=-tan pi csc(-pi)= -csc pi sec(-pi)=sec pi cot(-pi)=-cot pi

Graphs of the trigonometric functions ,the Inverse Sine, Cosine, and Tangent Functions.

Graphs of sine and cosine funtion : y=f(x)=sin x y=f(x)=cos x y=f(x)=tan x y=f(x)=csc x y=f(x)=secx y=f(x)=cotx

Tangent Functions y=tan-1 x and only if x=tan y Where - infinity< x< infinity and -pi/2

Cosine Function y=cos-1 x if and only if x= cos y where -1< x < 1 and 0 < y < pi

Inverse sine function y=sin-1 x if and only if x=sin y Where -1

Sine Law

Sin A/a=Sin B/b=Sin C/c SinA/a=SinB/b ; SinA/a=SinC/c ; SinB/b=Sinc/c A+B+C=180o

Properties of the trigonometric function

Determine the domain and rage

Domain Range Sin ARN [-1,1), -1< Sin pi<1 Cos ARN [-1,1] -1

sin=y scs=1/y cos = x sec=1/x tan=y/x cot=x/y

Angles and Trigonometric formulas

sin(900 -

The Unit Circle

https://matterofmath.com/trigonometry/unit-circle/

sin=opposite side /hypotenuse cos =adjacent side /hypotenuse tan =opposite side/adjacent side csc =hypotenuse/opposite side sec =hypotenuse/adjacent side cot=adjacent side/opposite side

Cosine Law

a2=b2+c2-2bc cos A b2=a2+c2-2ac Cos B c2=a2+b2-2ab Cos C