1. Bell Work R
Find the 6 trig functions for <R. sin R = csc R = cos R = sec R = tan R = cot R =
22 cm S T
14 cm

2. 5-3 Trigonometric Functions on the Unit Circle

3. More Special Triangles…Find the missing sides.1 1 ? ?
45°
60° ? ?

4. Our Goal today is to learn to use the Unit Circle to evaluate values of angles
The Unit Circle: A circle with a radius of 1 that is placed on the xy coordinate plane with center at the origin.

5. More Unit Circle
Find the sine, cosine, and tangent of a 30° angle using the unit circle.
Sin 30° =
Cos 30° =
Tan 30° =
Always draw the triangle to the x axis!!!
Always write the ordered pair, and the answer is in that point!!!!

6. More Unit Circle
Find the sine, cosine, and tangent of a 60° angle using the unit circle.
Sin 60° =
Cos 60° =
Tan 60° =
Always draw the triangle to the x axis!!!
Always write the ordered pair, and the answer is in that point!!!!

7. More Unit Circle
Find the sine, cosine, and tangent of a 45° angle using the unit circle.
Sin 45° =
Cos 45° =
Tan 45° =
Always draw the triangle to the x axis!!!
Always write the ordered pair, and the answer is in that point!!!!

8. More Unit Circle
Find the sine, cosine, and tangent of a 210° angle using the unit circle.
Sin 210° =
Cos 210° =
Tan 210° =
Always draw the triangle to the x axis!!!
Always write the ordered pair, and the answer is in that point!!!!

9. More Unit Circle
Find the sine, cosine, and tangent of a 150° angle using the unit circle.
Sin 150° =
Cos 150° =
Tan 150° =
Always draw the triangle to the x axis!!
Always write the ordered pair, and the answer is in that point!!!!

10. More Unit Circle
Find the sine, cosine, and tangent of a 600° angle using the unit circle.
Sin 600° =
Cos 600° =
Tan 600° =
Always draw the triangle to the x axis!!
Always write the ordered pair, and the answer is in that point!!!!

11. More Unit Circle
Find the sine, cosine, and tangent of a 225° angle using the unit circle.
Sin 225° =
Cos 225° =
Tan 225° =
Always draw the triangle to the x axis!!
Always write the ordered pair, and the answer is in that point!!!!

12. More Unit Circle
Find the sine, cosine, and tangent of θ using the unit circle.
Sin θ = y/1 = y
Cos θ = x/1 = x
Tan θ = y/x
These are always the ratios for an angle on the unit circle….but remember that the radius must be 1!!!

13. Signs in Each Quadrant. All Student Take Calculus (-, +) (+, +) (-, -)
(+, -)

14. Find each value using the Unit Circle.
Cos 210°
Sin 300°
Cos 135 °
Tan 480°

15. Build the Unit Circle

16. What about Reciprocal Functions?
Csc θ = 1/y (reciprocal of Sin θ) Sec θ = 1/x (reciprocal of Cos θ) Cot θ = x/y (reciprocal of Tan θ)

17. Find each value using the Unit Circle.
Sec -135°
Csc 660°
Cot 240 °
Sec -225°

18. What about Quadrantal Angles?
Sin 90°
Cos 90°
Tan 90 °
Csc 90 °
Sec 90 °
Cot 90 °

19. Find each value using the Unit Circle.
csc 270°
Sin -225°
Cot 495 °
Sec -240°

20. Values not on the unit circle.
Day 2
Values not on the unit circle.

21. Finding trig values when it is NOT a unit circle. (Radius is not one)
Trig Ratios
Sin θ = Csc θ =
Cos θ = Sec θ =
Tan θ = Cot θ =

22. Sin θ = Csc θ = Cos θ = Sec θ = Tan θ = Cot θ =
Find the values of the six trig functions for angle θ in standard position if a point with coordinates (5, -12) lies on its terminal side.
Sin θ = Csc θ =
Cos θ = Sec θ =
Tan θ = Cot θ =
Always draw the triangle to the x axis!!!

23. Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ=
Find the values of the six trig functions for angle θ in standard position if a point with coordinates (-3, -4) lies on its terminal side.
Sinθ= Csc θ=
Cosθ= Sec θ =
Tanθ= Cot θ=
Always draw the triangle to the x axis!!!

24. Sinθ= Csc θ= Cosθ= Sec θ = Tanθ= Cot θ=
Find the values of the six trig functions for angle θ in standard position if a point with coordinates (-4, 2) lies on its terminal side.
Sinθ= Csc θ=
Cosθ= Sec θ =
Tanθ= Cot θ=
Always draw the triangle to the x axis!!!

25. Sinθ= Cscθ= Cosθ= Secθ= Tanθ= Cotθ =
Suppose θ is an angle in standard position whose terminal side lies in Quadrant III. If sin θ = -4/5, find the values of the remaining five trig functions.
Sinθ= Cscθ=
Cosθ= Secθ=
Tanθ= Cotθ =

26. Sinθ= Csc θ= Cosθ= Secθ= Tanθ= Cotθ=
Suppose θ is an angle in standard position whose terminal side lies in Quadrant IV. If sec θ = √3, find the values of the remaining five trig functions.
Sinθ= Csc θ=
Cosθ= Secθ=
Tanθ= Cotθ=