a pencil highlighter red pen calculator notebook 1
a. pencil, highlighter, red pen, calculator, notebook 1. 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. c. 2. Draw a sketch of . Then find THREE angles that are coterminal with . total:
1. 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 an isosceles right Δ. a. y Therefore, It is a Δ. (45˚– 90˚ Δ) +1 θ +2 α 1 +1 x +1 +2 total:
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. b) In radians, it is a y Δ. ½ is the smallest side, so it must be opposite from the smallest angle, 30˚. θ x α +2 must be across from α = 60˚. 1 +1 +2
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) (1, 0) y +1 1 +2 x total:
2. Draw a sketch of θ. Then find THREE angles that are coterminal with θ. – 72˚ + 360 +1 288 o θ θ +1 x x +1 +1 – 72˚ – 360 – 432 o +1 +1 648 o or +1 – 792 o or ? +1 or or ? total:
Recall from previous lessons which trig functions are positive in each quadrant: Remember: All Students Take Calculus y y sin all II I tan III IV cos x x When we say 0 ≤ θ < 2π, we are considering ONE full rotation of the circle.
Example #1: Solve cos θ = for 0 ≤ θ < 2π. I and ___. IV cos θ > 0 in quadrants ___ QI solution. Draw a sketch of θ for the ____ Label the sides of the reference triangle. 30 – 60 – 90 Hint: It’s a ______ triangle. θ = 30° y x
Example #1: Solve cos θ = for 0 ≤ θ < 2π. QIV solution. Draw a sketch of θ and α for the ____ Label the sides of the reference triangle. This is the SAME reference triangle as in Q 1, just rotated. Therefore: Therefore, if we only know cos θ = there are 2 solutions: and y α for 0 ≤ θ < 2π, then x
Example #2: Solve cos θ = for 0 ≤ θ < 2π. II and ___. III cos θ < 0 in quadrants ___ QII y y α x α QIII x
Example #3: Solve sin θ = 0 for 0 ≤ θ < 2π. 0 then sin θ = 0 means y = ___. 0 Since sin θ = ___ and r > ___, 0 Where on a coordinate plane is y = ___? x–axis y x Work on the Practice.
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. cos θ < 0 in quadrants II and III. a) QII y y α x α QIII x
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. sin θ < 0 in quadrants III and IV. b) α QIII y y x α QIV x
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. tan θ < 0 in quadrants II and IV. c) QII α y y x α x QIV
Clear your desk except for a pencil, highlighter, and a calculator! After the quiz, work on the rest of the worksheet.
- Slides: 15