Trigonometric Identities - Miami
= sin 1+cos Double-Angle Formulas sin2 = 2sin cos cos2 = cos2 sin2 tan2 = 2tan 1 tan2 cos2 = 2cos2 1 cos2 = 1 2sin2 Product-to-Sum Formulas sinxsiny= 1 2 [cos(x y) cos(x+ y)] cosxcosy= 2 [cos(x y) + cos(x+ y)] sinxcosy= 1 2 [sin(x+ y) + sin(x y)] Sum-to-Product Formulas sinx+ siny= 2sin x+y 2 cos x y 2 sinx siny= 2sin x y 2 cos x+y 2 cosx+ cosy
Euler’s Formula and Trigonometry
sin is the y-coordinate of the point The picture of the unit circle and these coordinates looks like this: 1 (cos ;sin ) This is also true for the point z= i
Graphs of Sine and Cosine Functions
Our first point on the graph of y = sin x is thus y = sin 0 = 0 This is the point (0, 0) located at the origin of the graph If the circular point now moves a quarter of the way around the circle in a positive direction, arc x equals π/2 radians, the vertical component b of the circular point is equal to the radius r, and
TRIGONOMETRY LAWS AND IDENTITIES
TRIGONOMETRY LAWS AND IDENTITIES DEFINITIONS sin(x)= Opposite Hypotenuse cos(x)= Adjacent Hypotenuse tan(x)= Opposite Adjacent csc(x)= Hypotenuse Opposite sec(x)= Hypotenuse Adjacent
Complex numbers and Trigonometric Identities
(cos y, sin y) (cos (x –y), sin (x – y)) (1, 0) Figure 1 Figure 2 Find cos ????????−????????based on the unit circle Distance between the two labeled points
45 Graphs of Sine and Cosine Functions
y sin x 2 cos x cos x y a sin x b sin x sin x y a sin bx 2 y a sin x b > 1, 0 < b < 1, y a sin bx 2 y a sin bx x 0 x 2 b y a sin x x 0 x 2 , y 3 cos x, x y f x y 3 cos x y f x 324 Chapter 4 Trigonometry Period of Sine and Cosine Functions Let be a positive real number The period of and is given by Period 2 b b y a sin bx y a cos bx
Trig Cheat Sheet - Lamar University
cos hypotenuse q= hypotenuse sec adjacent q= opposite tan adjacent q= adjacent cot opposite q= Unit circle definition For this definition q is any angle sin 1 y q==y 1 csc y q= cos 1 x q==x 1 sec x q= tan y x q= cot x y q= Facts and Properties Domain The domain is all the values of q that can be plugged into the function sinq, q can be any
SOME BASIC TRIGONOMETRY - KNOW THIS FUNDAMENTAL
Cofunction Identities If x is measured in radians, then: sin(x)=cos π 2 −x cos(x)=sin π 2 −x We have similar relationships for tangent and cotangent - and for secant and cosecant; remember that they are sometimes undefined
Identidades Trigonom etricas Fundamentales
Identidades Trigonom etricas Fundamentales 1 csc(x) = 1 sin(x) 2 sec(x) = 1 cos(x) 3 tan(x) = sin(x) cos(x) 4 cot(x) = cos(x) sin(x) 5 1+tan2(x) = sec2(x) 6 1
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