1. Trig. Ratios in a Coordinate System
Chapter 6.2

2. A point on the terminal side of an angle θ is given
A point on the terminal side of an angle θ is given. Find the exact value of the six trigonometric functions of θ. y
opposite
sin  = =
hypotenuse r x
adjacent
cos  = =
hypotenuse r y
opposite
tan  = =
adjacent x

3. A point on the terminal side of an angle θ is given
A point on the terminal side of an angle θ is given. Find the exact value of the six trigonometric functions of θ. y
opposite
sin  = =
hypotenuse r x
adjacent
cos  = =
hypotenuse r y
opposite
tan  = =
adjacent x

4. A point on the terminal side of an angle θ is given
A point on the terminal side of an angle θ is given. Find the exact value of the six trigonometric functions of θ.
(-5, -8)

5. Unit Circle

6. Unit Circle - center is always at the origin and the radius is always 1.
(0,1)
opposite
sin  = = = y
hypotenuse 1
(x,y)
r = 1 
(-1,0)
(1,0) x
adjacent
cos  = = = x
hypotenuse 1 y
opposite
(0,-1)
tan  = =
adjacent x

7. The point given is a point on the unit circle
The point given is a point on the unit circle. Find the exact value of the six trigonometric functions of θ.
( , )

8. The point given is a point on the unit circle
The point given is a point on the unit circle. Find the exact value of the six trigonometric functions of θ.
( , )

9. We divide the unit circle into multiples of 45°.
90°
135°
45°
180° 0°
225°
315°
270°

10. We divide the unit circle into multiples of 45°.
90°
135°
45°
180° 0°
225°
315°
270°

11. We can also divide the unit circle into multiples of 30°.
90°
120°
60°
150°
30°
180° 0°
210°
330°
240°
300°
270°

12. We can also divide the unit circle into multiples of 30°.
90°
120°
60°
150°
30°
180°
30° 0°
210°
330°
240°
300°
270°

14. 1. sin 45° cos 180° 2. tan π/4 – sin 3π/2 3. sin 45° cos 45°
Find the exact value of the trigonometric expression.
1. sin 45° cos 180°
2. tan π/4 – sin 3π/2
3. sin 45° cos 45°
4. 2sin π/3 – 3tan π/6
5. 3csc π/3 + cot π/4

15. Using a calculator, find the approximate value of each.
1. Cos 48°
.67
2. Csc 21°
2.79
3. Tan π/12
.27
4. Sec π/3 2