Pre-Calc Chapter 7 trigonometry concepts
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| standard position | vertex is at the origin, initial side is along the positive x-axis
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| coterminal angles | in std. position have the same terminal ray. to find these add or subtract 360 degrees or 2pi radians
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| revolution | a common unit for measuring ver large angles. it is a complete circular motion
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| degrees | a common unit for measuring smaller angles. 360 degrees equals one revolution
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| 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
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| if theta is in degrees S= | (theta/360)(2*pi*r)
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| if theta is in degrees K= | (theta/360)(pi*r^2)
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| if theta is in radians S= | theta*r
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| if theta is in radians K= (first equation) | (1/2)(r^2 * theta)
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| if theta is in radians K= (second equation) | (1/2)(rs)
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| sin(theta)= | y/r where r can not = 0
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| cos(theta)= | x/r where r can not = 0
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| quadrantal angles | an angle in standard position with the terminal ray along an axis
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| Domain and Range sin(theta) | D theta is an element of real #s R -1 <(=) y (<=) 1
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| Domain and Range cos(theta) | D theta is an element of real #s R -1 <(=) y (<=) 1
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| referance angle | an angle theta that is the acute positive angle formed by the terminal ray of theta and the x-axis
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| Earth's rotation speed in mi/h | 1038cos(x)
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| # of ft in a mile | 5280
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| earth's circumference | 3963 mi
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| Domain and Range restricted sin | D -90 degrees <(=) x <(=) 90 degrees R -1 <(=) y <(=) 1
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| Domain and Range Inverse sin | D -1 <(=) x <=) 1 R -90 degrees <(=) y <(=) 90 degrees
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| Domain and Range restriced tan | D -90 degrees <(=) x <(=) 90 degrees R y is an element of all real #s
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| Domain and Rang Inverse tan | D x is an element of all real #s R -90 degrees <(=) y <(=) 90 degrees
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| Domain and Range restricted cos | D 0 <(=) x <(=) 180 degrees R -1 <(=) y <=) 1
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| Domain and Range Inverse cos | D -1 <(=) x <=) 1 R 0 <(=) y <(=) 180 degrees
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| tan theta= | (sin theta/ cos theta) y/x where x does not = 0
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| csc theta= | (1/ sin theta) r/y where y does not = 0
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| sec theta= | (1/ cos theta) r/x where x does not = 0
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| cot theta= | (1/ tan theta) (cos theta/ sin theta) x/y where y does not = 0
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| what are restrictions on csc? | y can't = 0
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| what are restrictions on sec? | x can not = 0
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| what are restrictions on tan? | x can not = 0
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| what are restrictions on cot? | y can not = 0
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