Mirian Zaruma

What to know…RadiansReference anglesCoterminal anglesSpecial anglesTrig. formulas

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

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.

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

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

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.

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.

See it wasn’t that bad.This is just the basic later on

you’ll learn trig. identify other topics of trigonometry.