U8D8 pencil, highlighter, red pen, calculator, notebook Have out: Bellwork: Given the point (1, ) on the terminal side of θ, Plot the point Show θ and α Draw the reference triangle Label x, y, and r. Find sinθ, cosθ, and tanθ. Find θ in radians +1 y +2 +1 +1 θ x α total:

Given the point (1, ) on the terminal side of θ, v) Find sinθ, cosθ, and tanθ. vi) Find θ in radians +2 Note the ratio of the sides. It’s a special right triangle +2 y +2 Recall: 60 = θ x +1 α 60 30 +2 total:

 Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . = 0˚ y = 0 ( , ) 1 1 x

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 . b) = 90˚ is the same as what degree? y ( , ) 1 1 θ = undefined x

 Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . = 180˚ y θ = 0 1 x ( , ) –1

 Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of . = 270˚ y θ = undefined x 1 ( , ) –1

Recall from yesterday: Given reference angle , and . Given reference angle , and . Given reference angle , and . Notice that the denominators are always equal to 2. Notice that and have the cosine and sine values switched. Let’s put it all together using some patterns:

θ Fill in the values for common angles. sinθ cosθ tanθ = 0 = 1 = 1 = 0 sinθ cosθ tanθ = 0 = 1 = 1 = 0 = 0 1 = undefined Use the identity to find tanθ.

The reference Δ is an isosceles right Δ. Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) a) The reference Δ is an isosceles right Δ. Therefore, It is a Δ. (45˚–45˚–90˚ Δ) y x 1 θ

Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) b) (0, 1) y x 1 θ

The reference Δ is a 30˚–60˚–90˚ Δ. Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) c) The reference Δ is a 30˚–60˚–90˚ Δ. In radians, it is a Δ. y x ½ is the smallest side, so it must be opposite from the smallest angle, 30˚. 1 θ

The reference Δ is a 30˚–60˚–90˚ Δ. d) Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) The reference Δ is a 30˚–60˚–90˚ Δ. d) In radians, it is a Δ. y x ½ is the smallest side, so it must be opposite from the smallest angle, 30˚. 1 θ must be across from α = 60˚. α

It’s time for the… Quiz Clear your desks except for a pencil and highlighter. When finished, flip your quiz over, we are going to grade the quiz in class in a few minutes. Your assignment: Finish the worksheets.

Take out a red pen, it’s time to grade the quiz.

90˚ 120˚ 60˚ 135˚ 45˚ 150˚ 30˚ 0˚ Each answer is 1 point. 180˚ 360˚ y 60˚ 135˚ 45˚ 150˚ 30˚ 0˚ Each answer is 1 point. x 180˚ 360˚ 210˚ 330˚ 225˚ 315˚ 240˚ 300˚ 270˚

Finish the practice worksheets