Using the Unit Circle
Special Triangle Review
o Reference Angles: o Reciprocal Trig Functions csc 𝜃 sec 𝜃 cot 𝜃 Building the Unit Circle
Assume there exists a circle with radius 1 centered around the origin. This is called the __________. 1. Fill in the following important reference angles in both degrees and radians. 2. Use knowledge of special right triangles to find the sine and cosine values at the given angles. sin 30 = sin 45 = sin 60 = cos 30 = cos 45 = cos 60 = tan 30 = tan 45 = tan 60 = 3. Fill in the coordinates where the angle’s ray meets the unit circle. Explain WHY. sin 𝜃 = SO… csc 𝜃 = cos 𝜃 = SO… sec 𝜃 = tan 𝜃 = SO… cot 𝜃 = 4. Use your completely filled out unit circle to complete the following table: Trig Value Puzzle Square
Practice!
Use the Unit Circle to determine the exact value of each. Then give the decimal value.
c) cos π
π
b) sin120°
a) cos
d)
tan315°
h)
csc360°
4
e)
sec225°
i) sin -120°
f)
sin
3π
2
ii) cos− π
4
g)
sin
5π
3
iii) sin − 11π
6
iv) tan-150°