1. pencil, red pen, highlighter, calculator, notebook
U8D6
Have out:
Fill in the degrees and radian equivalent for all angles between 0° and 360° that are multiples of 30° and 45°. (Simplify all radians.)
Bellwork: y
Can you guess what your quiz will be on today???
Try to complete the bellwork WITHOUT looking at your notes. x
When finished, work on Practice #1 of the worksheet.
total:

2. +1 each correct degree & radian
90˚
120˚ y
60˚
135˚
45˚
150˚
30˚ 0˚ x
180˚
360˚
210˚
330˚
225˚
315˚
240˚
300˚
270˚
total:

3. Finding  and the Trig Equations
Practice #1: For each example, the given point is on the terminal side of . Complete the following:
(iv) Label x, y, and r.
(i) Plot the point.
(v) Determine sin, cos, and tan.
(ii) Show  and α.
(iii) Draw the reference triangle.
(vi) Approximate .

4. BTW, couldn’t we just have used special right triangles?
Practice #1: For each example, the given point is on the terminal side of . Complete the following:
BTW, couldn’t we just have used special right triangles?
Look at the ratios.
(iv) Label x, y, and r.
(i) Plot the point.
(v) Determine sin, cos, and tan.
(ii) Show  and α.
(iii) Draw the reference triangle.
(vi) Approximate .
1) (–2, ) y  α x

5. Once again, couldn’t we just have used special right triangles?
Practice #1: For each example, the given point is on the terminal side of . Complete the following:
Once again, couldn’t we just have used special right triangles?
Look at the ratios.
(iv) Label x, y, and r.
(i) Plot the point.
(v) Determine sin, cos, and tan.
(ii) Show  and α.
(iii) Draw the reference triangle.
(vi) Approximate .
2) (3, –3) y  x α

6. Practice #2: Draw  in each quadrant
Practice #2: Draw  in each quadrant. Show the reference triangle, α, and label x, y, and r. y y QI
QII r r y y   α x x x –x y y
QIII
QIV   –x x x x α α –y –y r r

7. > < > > < > < <
Practice #3: Insert the correct inequality symbol.
(r > 0 for all quadrants) y y QI
QII
>
<
x __ 0
x __ 0
>
y __ 0
>
y __ 0 x x
QIII y
QIV y x x
<
>
x __ 0
x __ 0
<
<
y __ 0
y __ 0

8. ALL STUDENTS TAKE CALCULUS sin all tan cos
Conclusion: Given sin, cos, and tan, which are positive in each quadrant? y
sin
all II I x
III IV
There is a mnemonic to help you remember which functions are positive in each quadrant:
tan
cos
ALL
STUDENTS
TAKE
CALCULUS
________________________________________

9. Practice #4: Answer the following:
1) If and , find cos, and tan, and .
This means the terminal side of  is in QIII.
Our answer is in radians because the problem starts in radians. Be on the lookout for this scenario whenever you solve future problems.
Make sure your calculator is in radian mode! y  x α
To find  , pick the positive trig equation.
(Our answer is in radians)

10. 2) If and , find sin, and tan, and .
This means the terminal side of  is in QIV. y  x α

11. 2) If and , find sin, and tan, and .
Look at the ∆. Anything “special”?
It is a 30–60–90 ∆. y
α is across from the long leg, so it is 60 . 
Recall: 60 = x α

12. 3) If tan = 1 and , find sin and  (in radians).
In which quadrant is tangent positive and cosine negative?
QIII y  x α

13. 3) If tan = 1 and , find sin and  (in radians).
Look at the ∆. It may be hard to notice, but is there anything “special”?
It is an isosceles right ∆. y
Therefore it is a 45–45–90 ∆.
α is across from a leg, so it is 45 . 
Recall: 45 = x α

14. 4) If and tan = –2, find sin, and cos, and .
This means the terminal side of  is in QII. y  α x
To find  , pick the positive trig equation.

15. Finish the practice worksheets