1. U8D4
Have out:
pencil, red pen, highlighter, notebook, calculator, assignment
Bellwork:
1. Convert the following angles from degrees to radians.
a) 30
b) 45 +2 +2
2. Convert the following from radians to degrees. a) b) +2 +2
total:

2. Radian Values for Common Angles
Part 1: Record the degree measures for all multiples of 30° and 45°.
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
Use a pencil!!!
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

3. Radian Values for Common Angles
Part 2: Radians. Use multiples of these values to fill in the radian equivalent for each angle.
90˚
120 ˚
60˚
135 ˚
45˚
30° =
150 ˚
30˚
45° =
180 ˚ 0˚
360 ˚
on the bottom of the worksheet
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

4. now reduce the fractions
30° =
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
now reduce the fractions
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

5. 30° =
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

6. now reduce the fractions
45° =
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
now reduce the fractions
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

7. 45° =
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

8. This will be your first quiz on Tuesday!!!
90˚
120 ˚
60˚
135 ˚
45˚
150 ˚
30˚
Memorize this diagram.
This will be your first quiz on Tuesday!!!
180 ˚ 0˚
360 ˚
210 ˚
330 ˚
225 ˚
315 ˚
300 ˚
240 ˚
270 ˚

9. Label the sides of the right triangle.
Example # 1:
The point (3, 4) is on the terminal side of angle θ in standard position. Plot (3, 4) and draw θ. y x
Let r be the length of the segment from (3, 4) to the origin. r 4
Draw a vertical segment from (3, 4) to the x–axis. This is called the ________ ________. θ
reference
triangle 3
Label the sides of the right triangle.
x = _____ and y = _____ 3 4

10. Determine r using the Pythagorean Theorem. r2 = (___)2 + (___)2 3 4
Example # 1:
Determine r using the Pythagorean Theorem.
r2 = (___)2 + (___)2 3 4 y x
r2 = ___ 25
r = ___ 5 r
= 5 4
Use an ________ trigonometric function to approximate θ.
inverse θ
Put your calculator in “radian” mode. 3 4
Make sure you know what mode the calculator is in! 5 3
0.93
radians 5 4
53.13 3
Now put your calculator in “degree” mode

11. The point (–3, 4) is on the terminal side of angle θ.
Example # 2:
The point (–3, 4) is on the terminal side of angle θ.
Draw the ________________, and label x, y, and r.
reference triangle
reference angle
Label the acute angle at the origin α, the _______________.
This reference triangle is __________ to the reference triangle in Example # 1, so
congruent y x
α = ______
53.13 r
= 5
180˚
53.13
126.87 4
= 
53.13 -3

12. Example # 2:
Since 90°< ____ < 180°, θ is a ____________ angle. Use your calculator to approximate the following:
Quadrant II
Check the mode, people!
126.87˚
0.80 y x
126.87˚ r
= 5
–0.60 4
= 
53.13 -3
126.87˚
–1.33

13. In quadrant II, sinθ > _____, cosθ < ____, and tanθ < _____
Use x, y, and r on the reference triangle to find: 4 5 y x r
= 5 - 3 4
=  5
53.13 -3 4 - 3

14. Practice: Draw angle θ in each quadrant
Practice: Draw angle θ in each quadrant. Draw θ, the reference triangle, and α. QI
QII
QIII
QIV r r θ y y θ θ x θ α –x x –x α α –y –y r r
θ = α
θ = 180 – α
θ = α
θ = 360 – α

15. ____ ____ ____ ____ ____ ____ ____ ____ ____
No matter which quadrant θ is in, the definitions for sinθ, cosθ, and tanθ are all the same.
There is a mnemonic (similar to SOH CAH TOA) to help you remember these definitions.
____ ____ ____ ____ ____ ____ ____ ____ ____ s y r c x r t y x
pronounced:
“Sir Kix-er Tix” y θ x

16. In quadrant III sinθ < ____, cosθ < _____, and tanθ > ____.
Practice: The point (–3, –4) is a point on the terminal side of angle θ. Draw the reference triangle. Label the sides x, y, and r. Determine: - 4 y x
≈ 53.13˚ 5
Check the mode, people! - 3
≈ 53.13˚ 5 θ –3 -4 4 = α -3 3
≈ 53.13˚ –4 5
180 + α
≈ 180 
≈ 
Note: when you are finding α you can ignore the negative signs, or just use the positive ratio (e.g. tangent in this case).
In quadrant III sinθ < ____, cosθ < _____, and tanθ > ____.

17. ♫ What rolls down stairs… ♪
Finish the worksheets
All kids love logs
♫ What rolls down stairs… ♪