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Pre-Calc Chapter 7

Pre-Calc Chapter 7 trigonometry concepts

standard position vertex is at the origin, initial side is along the positive x-axis
coterminal angles in std. position have the same terminal ray. to find these add or subtract 360 degrees or 2pi radians
revolution a common unit for measuring ver large angles. it is a complete circular motion
degrees a common unit for measuring smaller angles. 360 degrees equals one revolution
radians when the arc of a circle has the same length as the radius of the circle, the measure of the central angle is 1 radian
if theta is in degrees S= (theta/360)(2*pi*r)
if theta is in degrees K= (theta/360)(pi*r^2)
if theta is in radians S= theta*r
if theta is in radians K= (first equation) (1/2)(r^2 * theta)
if theta is in radians K= (second equation) (1/2)(rs)
sin(theta)= y/r where r can not = 0
cos(theta)= x/r where r can not = 0
quadrantal angles an angle in standard position with the terminal ray along an axis
Domain and Range sin(theta) D theta is an element of real #s R -1 <(=) y (<=) 1
Domain and Range cos(theta) D theta is an element of real #s R -1 <(=) y (<=) 1
referance angle an angle theta that is the acute positive angle formed by the terminal ray of theta and the x-axis
Earth's rotation speed in mi/h 1038cos(x)
# of ft in a mile 5280
earth's circumference 3963 mi
Domain and Range restricted sin D -90 degrees <(=) x <(=) 90 degrees R -1 <(=) y <(=) 1
Domain and Range Inverse sin D -1 <(=) x <=) 1 R -90 degrees <(=) y <(=) 90 degrees
Domain and Range restriced tan D -90 degrees <(=) x <(=) 90 degrees R y is an element of all real #s
Domain and Rang Inverse tan D x is an element of all real #s R -90 degrees <(=) y <(=) 90 degrees
Domain and Range restricted cos D 0 <(=) x <(=) 180 degrees R -1 <(=) y <=) 1
Domain and Range Inverse cos D -1 <(=) x <=) 1 R 0 <(=) y <(=) 180 degrees
tan theta= (sin theta/ cos theta) y/x where x does not = 0
csc theta= (1/ sin theta) r/y where y does not = 0
sec theta= (1/ cos theta) r/x where x does not = 0
cot theta= (1/ tan theta) (cos theta/ sin theta) x/y where y does not = 0
what are restrictions on csc? y can't = 0
what are restrictions on sec? x can not = 0
what are restrictions on tan? x can not = 0
what are restrictions on cot? y can not = 0
Created by: classicsgrl6