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What to know… Radians Reference angles Coterminal angles Special angles Trig. formulas
Radians ,[object Object],[object Object],[object Object],[object Object],[object Object],40⁰ 0.6981 • 180 ∏ = 39 round  off to 40 radian • 180 ∏ 40 • ∏ 180 =0.689 degree•∏ 180
Reference angles ,[object Object],Subtract from 360 only when the given angle is more than 360. Remember a reference angle is  always  an acute angle. 135⁰ x 135+x=180 x=180-135 x=45
Coterminal angles ,[object Object],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) 200⁰ x Standard position Since 200 ⁰ is a little over 180 ⁰ just subtract the two. 200=180+x 20=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 angles These angles have an exact value. Whenever you see them use these values Θ 0⁰ 30⁰ 45⁰ 60⁰ 90⁰ 180⁰ 270⁰ 360⁰ sin Θ 0 1/2 √ 2/2 √ 3/2 1 0 -1 0 cos Θ 1 √ 3/2 √ 2/2 1/2 0 -1 0 1 tan Θ √ 3/3 1 √ 3 undefined 0 undefined 0
Trig. Formulas SohCahToa Sin=opposite over hypotenuse Cosine=adjacent over hypotenuse Tangent= opposite over adjacent Tan  θ =  y  = sin θ x  cos  θ This is your first trig.  formula. P(x,y) y x θ 1 Sin θ =  y 1 Cos θ  =  x 1 Tan θ =  y x Point P coordinates are (cos  θ ,sin  θ )
Reciprocals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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.

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TRIG REFERENCE

  • 2. What to know… Radians Reference angles Coterminal angles Special angles Trig. formulas
  • 3.
  • 4.
  • 5.
  • 6. Special angles These angles have an exact value. Whenever you see them use these values Θ 0⁰ 30⁰ 45⁰ 60⁰ 90⁰ 180⁰ 270⁰ 360⁰ sin Θ 0 1/2 √ 2/2 √ 3/2 1 0 -1 0 cos Θ 1 √ 3/2 √ 2/2 1/2 0 -1 0 1 tan Θ √ 3/3 1 √ 3 undefined 0 undefined 0
  • 7. Trig. Formulas SohCahToa Sin=opposite over hypotenuse Cosine=adjacent over hypotenuse Tangent= opposite over adjacent Tan θ = y = sin θ x cos θ This is your first trig. formula. P(x,y) y x θ 1 Sin θ = y 1 Cos θ = x 1 Tan θ = y x Point P coordinates are (cos θ ,sin θ )
  • 8.
  • 9. See it wasn’t that bad. This is just the basic later on you’ll learn trig. identify other topics of trigonometry.