The Unit Circle And Finding Exact Value (Using The Uc) Worksheet
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15.1 / 5.2 – The Unit Circle and Finding Exact Value (using the UC)
- wrapping function → a function that pairs ____________________ to a ________ on the unit circle
- unit circle → a circle with a ___________ centered at the _________ and has equation _____________
• cosine function → _____________________
• sine function → ____________________
• terminal point → ______________________
• reference number → __________________
Refer to TRIG CHART / UNIT CIRCLE SHEET to label parts of the Unit Circle:
1.) Complete the TRIG CHART → Use the 45 – 45 – right ∆ and the 30 – 60 – right ∆
For quadrant angles (0° and 90°), use your calculator
2
3
2
3
(Make sure to rationalize the denominator → EXAMPLE:
)
⋅
=
3
3
3
2.) Label the degree measure ABOVE each pt on the Unit Circle (only use increments of 30°, 45°, 60°)
3.) Label the radian measure BELOW each pt on the Unit Circle (convert degree measure to radians)
4.) Draw diagonal lines through pairs of points that have the same reference number (angle):
a.) 30° and 210°
b.) 45° and 225°
c.) 60° and 240°
Ref Angle
Ref Angle
Ref Angle
150° and 330°
135° and 315°
120° and 300°
= 30°
= 45°
= 60°
5.) Label the terminal point (x , y) of each degree/radian measure → (x = cos θ , y = sin θ)
(Remember: cosine is only positive in Quads I and IV ; sine is only positive in Quads I and II)
6.) Also add the following to your TC/UC sheet: Quadrant #’s and where trig functions are positive
Steps to Find Exact Value of an Angle: Some answers contain radicals (NO decimal answers)
1.) Find the reference angle B – Use the “Coloring Coding key” to help determine this.
2.) Use Trig Chart to look up value using reference angle B.
3.) Use “Signs” Diagram of Trigonometric Functions to determine is value is positive or negative
* If finding the exact value of a quadrant angle (90°, 180°, 270°, or 360°) → use CALCULATOR
Examples: Using your TC/UC Sheet, find the exact value. Remember – NO DECIMALS!!!!
1.) sin 135° = _______
2.) csc 210° = _______
3.) cos 270° = _______
4.) tan – 780° = ______
5.) sec 390° = _______
6.) cot 180° = _______
7.) sin 240° = _______
8.) sec 150° = _______
7
π
5
π
7
π
7
π
9.)
= _______ 10.)
= ______ 11.)
= ______
12.)
= ____
tan
cos
sin
cot
−
6
3
2
4
π
8
π
π
15
13
(
)
14.)
= ______
sec −
2
π
13.)
= ______
15.)
= ______ 16.)
= _____
sin
csc
sec
−
4
6
3
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