580 likes | 795 Views
The Unit Circle. Chapter 3 Section 3. Unit circle circle with center at the origin and radius of 1 unit. radius 1 unit. r = 1 unit. y. y. x. x. Think: COFUNCTION THEOREM sin 30 = cos 60 c os 30 = sin 60. CIRCLE. UNIT. Use the unit circle to find: sin 30° = cos 45° =
E N D
The Unit Circle Chapter 3 Section 3
Unit circle circle with center at the origin and radius of 1 unit radius 1 unit r = 1 unit y y x x
Think: COFUNCTION THEOREM sin 30 = cos 60 cos 30 = sin 60
CIRCLE UNIT
Use the unit circle to find: sin 30° = cos 45° = cos 240° = sin 90° = cos 270° =
Use the unit circle to find: F. sec 330° = G. csc 270° = H. sec = I. csc = J. csc 180° =
To find tangent and cotangent, use. . . RATIO IDENTITIES in the unit circle in the unit circle
Use the unit circle to find: K. tan 30° = L. tan 150° = M. tan = N. cot = O. cot 90° = Most calculators won’t perform this operation, mistakenly giving an error message instead of zero!
ALL S We can use the unit circle to find angles. Consider the problem In which quadrants is the sine negative? In those quadrants, where is sine = ? Given the constraints , then T C Recall: sine is y!
Consider the problem In which quadrants is the sine positive? In those quadrants, where is sine = ? remember: radians! Given no other constraints , then
Use the unit circle to find θ if: P. Q. R. S.
On a graphing calculator: Parametric (FuncParPolSeq) Degree (Radian Degree) MODE x1T = cosT (x,T,θ,n) y1T = sin T (x,T,θ,n) y= Tmin = 0° Xmin = -1.5Ymin = -1.5 Tmax = 360° Xmax = 1.5 Ymax = 1.5 step = 15° Xscl = 1 Yscl = 1 WINDOW ZOOM Zoom Square TRACE Use for counterclockwise
P(x,y) sine cosine
P(x,y) line radius sine cosine
P(x,y) line radius sine cosine
P(x,y) line radius sine cosine
P(x,y) line radius sine cosine
P(x,y) line radius sine cosine
P(x,y) tangent radius sine cosine
cotangent P(x,y) tangent radius sine cosine
cotangent P(x,y) tangent radius sine cosine line