U8D7 pencil, highlighter, red pen, calculator, notebook Have out: Bellwork Simplify each expression. +1 (x – 3)(x + 3) (x – 1)(x – 4) +1 1) 2) +1 x(x – 1) (x – 3)(x + 7) +1 +1 +1 +4 +3 +2 total:

Coordinates of the Unit Circle y x ( , ) (x, y) θ If the radius r = 1 of the circle on the left, then the circle is called an _______ _______. 1 unit circle 1 -1 Let (x, y) be the point on the unit circle on the terminal side of θ. Fill in the coordinates for (x, y) for the quadrantal angles in an unit circle. -1

Coordinates of Common Angles Find the values of the legs of a 30° – 60° – 90°  if the hypotenuse is equal to 1. In radians, 30° – 60° – 90°  is a ____ – ____ – ____ . 30° 60° 2 _ 2 1 1 _ 2 _ 2 How can you make 2 →1? Convert degrees to radians. Divide all sides by 2.

In radians, 45° – 45° – 90°  is a ____ – ____ – ____ . Find the values of the legs of a 45° – 45° – 90°  if the hypotenuse is equal to 1. In radians, 45° – 45° – 90°  is a ____ – ____ – ____ . 45° 1 1 45° 1 How can you make →1? Divide all sides by . Convert degrees to radians.

Animation ( , ) Since and , for an ____ ______, when r = 1, then x = ______ and y = _______. unit circle cos θ sin θ x y ( , ) cos θ sin θ y _______ x ______ To help you remember which comes first, think alphabetical order! x before y c before s Animation

is the same as what degree?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . a) = 30˚ is the same as what degree? y 1 ( , ) 1 60˚ θ 30˚ x

What is the reference angle? b) = 30˚ y  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . What is the reference angle? b) = 30˚ y ( , ) 1 θ 1 60˚ 30˚ x

What is the reference angle? c) = 30˚ y  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . What is the reference angle? c) = 30˚ y x θ 1 30˚ 60˚ 1 ( , )

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . d) What is the reference angle? = 30˚ y 1 θ x 30˚ 60˚ 1 ( , )

is the same as what degree?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . a) = 45˚ is the same as what degree? 1 y x θ ( , ) 1 45˚ . 45˚

What is the reference angle? b) = 45˚ y  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . What is the reference angle? b) = 45˚ y ( , ) 1 1 θ 45˚ 45˚ x

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . c) What is the reference angle? y = 45˚ 1 θ x 45˚ 45˚ 1 ( , )

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . d) What is the reference angle? y = 45˚ 1 θ x 45˚ 1 45˚ ( , )

is the same as what degree?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . a) = 60˚ is the same as what degree? y ( , ) 1 1 30˚ θ 60˚ x

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . b) What is the reference angle? y = 60˚ ( , ) 1 1 θ 30˚ 60˚ x

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . c) What is the reference angle? = 60˚ y θ 1 x 60˚ 30˚ 1 ( , )

What is the reference angle?  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . d) What is the reference angle? = 60˚ y 1 θ x 60˚ 1 30˚ ( , )

Quotient Identity  Write the definitions of sinθ, cosθ, and tanθ in terms of x, y, & r. Remember “sir kix-er tix”? s y r c x r t y x __ __ __ __ __ __ __ __ __ You don’t say! ÷ Therefore:

Practice: 1) For each angle θ, find sinθ, cosθ, and tanθ. Convert radians to degrees if it helps, but try to “think in radians” as much as possible. a) = 45˚ Refer back to today’s notes to help you solve these problem if you get stuck. y x ( , ) 1 45˚ . θ 45˚ = 1

Practice: 1) For each angle θ, find sinθ, cosθ, and tanθ. d) = 210˚ y x θ . 30˚ 60˚ 1 ( , )

This means that the terminal side of θ is in QIII. a) 2) For each angle θ, find θ (in radians) and the other two values for trig ratios. This means that the terminal side of θ is in QIII. a) Make sure your calculators are in radian mode. y x θ . α y= –1 θ = π + α r = 4 θ ≈ π + 0.25 θ ≈ 3.39

Sine is positive and tangent is negative. e) 2) For each angle θ, find θ (in radians) and the other two values for trig ratios. Sine is positive and tangent is negative. e) This can only happen in QII. y x r = 3 θ y = 2 α . θ = π – α θ ≈ π – 0.73 θ ≈ 2.42

Work on the rest of the worksheets