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Mirian Zaruma
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What to know…RadiansReference anglesCoterminal anglesSpecial anglesTrig. formulas
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Radians-Radians are specific angles that are measured by the length around a circular path.-How do to find degrees in radian.-Radian =
-Turning radians into degrees.
40⁰
0.6981 • 180 ∏
= 39 round off to 40radian • 180 ∏
40 • ∏ 180
=0.689degree•∏ 180
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Reference angles-Reference angles are acute angles that are formed by the
terminal side and x-axis.
135⁰x
135+x=180 x=180-135 x=45
Subtract from 360 only when the given angle is more than 360.Remember a reference angle is always an acute angle.
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Coterminal angles-Coterminal angles are angles sharing the same initial and terminal side.
Unit circle- meaning each side equals to 1 as well as the hypotenuse. Purple arrow is the initial side(the beginning)Red arrow is the terminal side(the final result)
200⁰x
Standard positionSince 200 ⁰ is a little over 180 ⁰ just subtract the two.200=180+x20=x
If the degree is positive move counterclockwise on the unit circle.If its negative move clockwise on the unit circle.
135 ⁰
-225 ⁰
Example of Coterminal angles
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Special anglesΘ 0⁰ 30⁰ 45⁰ 60⁰ 90⁰ 180⁰ 270⁰ 360⁰
sinΘ 0 1/2 √2/2 √3/2 1 0 -1 0
cosΘ 1 √3/2 √2/2 1/2 0 -1 0 1
tanΘ √3/3 1 √3 undefined
0 undefined 0
These angles have an exact value. Whenever you see them use these values
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Trig. Formulas
P(x,y)y
xθ1
Sinθ= y 1Cosθ = x 1Tanθ= y xPoint P coordinates are (cos θ,sin θ)
SohCahToaSin=opposite over hypotenuseCosine=adjacent over hypotenuseTangent= opposite over adjacent
Tan θ= y = sinθ x cos θThis is your first trig. formula.
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Reciprocals
Cosecant θ or csc θ= 1 sinθsecant θ or sec θ = 1
cos θcotangent θ or cot θ= 1
tan θ
Cosecant is the reciprocal of sin.
Secant is the reciprocal of cosine.
Cotangent is the reciprocal of tangent.
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See it wasn’t that bad.This is just the basic later on
you’ll learn trig. identify other topics of trigonometry.