1. Lesson
12.2

2. Your Notes

6. Draw Angles in Standard Position
Example 1
Draw Angles in Standard Position
Draw an angle with the given measure in standard position.
215° a.
410° b.
60° c. –
SOLUTION a.
Because 215° is 35° more than 180°, the terminal side is 35° counterclockwise
past the negative x-axis. 6

7. Draw Angles in Standard Position
Example 1
Draw Angles in Standard Position b.
Because 410° is 50° more than 360°, the terminal side makes one whole revolution
counterclockwise plus 50° more. c.
Because 60° is negative, the
terminal side is 60° clockwise from the positive x-axis. – 7

8. Draw Angles in Standard Position
Checkpoint
Draw Angles in Standard Position
Draw an angle with the given measure in standard position.
30° 1. –
ANSWER

9. Draw Angles in Standard Position
Checkpoint
Draw Angles in Standard Position
Draw an angle with the given measure in standard position.
460° 2.
ANSWER

10. Draw Angles in Standard Position
Checkpoint
Draw Angles in Standard Position
Draw an angle with the given measure in standard position.
230° 3.
ANSWER

11. Draw Angles in Standard Position
Checkpoint
Draw Angles in Standard Position 4.
Draw an angle with measure 90° in standard position. On a different coordinate grid, draw an angle with measure 90° not in standard position.
ANSWER

12. Find Coterminal Angles
Example 2
Find Coterminal Angles
Find one positive angle and one negative angle that are coterminal with the given angle. a.
45° – b.
395°
SOLUTION
There are many correct answers. Choose a multiple of 360° to add or subtract. a. =
45° –
360° +
315°
405° 12

13. Find Coterminal Angles
Example 2
Find Coterminal Angles b.
395° –
360°
35° =
395° – 2 (
360° (
325° = – 13

14. Find Coterminal Angles
Checkpoint
Find Coterminal Angles
Find one positive angle and one negative angle that are coterminal with the given angle. 5.
50°
ANSWER
410°, ° – 6.
375°
ANSWER
15°, ° – 7.
70° –
ANSWER
290°, ° –

15. Evaluate Trigonometric Functions Given a Point
Example 3
Evaluate Trigonometric Functions Given a Point
Let be a point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of . ( ) 4, – 3
SOLUTION
Use the Pythagorean theorem to find the value of r. = r 42 + ( )2 3 –
x 2
y 2 25 5
Find the value of each function using x 4, y , and r = – = r y
sin 5 3 – x
cos 4
tan 15

16. Evaluate Trigonometric Functions Given a Point
Checkpoint
Evaluate Trigonometric Functions Given a Point 8.
Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of . ( )
3, 4 –
ANSWER =
sin 5 4 ,
cos 3 –
tan

17. Evaluate Trigonometric Functions Given a Point
Checkpoint
Evaluate Trigonometric Functions Given a Point 9.
Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of . ( )
6, 8
ANSWER =
sin 5 4 ,
cos 3
tan

18. Evaluate Trigonometric Functions Given a Point
Checkpoint
Evaluate Trigonometric Functions Given a Point
10.
Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of . – ( ) 15 8,
ANSWER =
sin ,
cos 17 8 – 15
tan

19. q q q q q Trigonometric Functions of a Quadrantal Angle Example 4
Evaluate the sine, cosine, and tangent functions of °. = q
SOLUTION
When °, you know that x r and y = – q = r y
sin q = r x
cos – 1 q = x y
tan r – q 19

20. Positive and Negative Trigonometric Functions
Example 5
Positive and Negative Trigonometric Functions
Determine whether the sine, cosine, and tangent functions of the given angle are positive or negative. a. b. c. d. 20

21. Positive and Negative Trigonometric Functions
Example 5
Positive and Negative Trigonometric Functions
SOLUTION
Because the terminal side lies in Quadrant II, sin 100° is positive, cos 100° is negative, and tan 100° is negative. a.
Because the terminal side lies in Quadrant I, sin 75° is positive, cos 75° is positive, and tan 75° is positive. b.
Because the terminal side lies in Quadrant III, sin 210°
Is negative, cos 210° is negative, and tan 210° is
positive. c.
Because the terminal side lies in Quadrant IV, sin 320° is negative, cos 320° is positive, and tan 320° is negative. d. 21

22. q Positive and Negative Trigonometric Functions Checkpoint 11.
Evaluate the sine, cosine, and tangent functions of °. = q
ANSWER
sin 90° 1, cos 90° , tan 90° is undefined =
Determine whether the sine, cosine, and tangent functions of the angle are positive or negative.
12.
40°
ANSWER
all positive

23. Positive and Negative Trigonometric Functions
Checkpoint
Positive and Negative Trigonometric Functions
Determine whether the sine, cosine, and tangent functions of the angle are positive or negative.
13.
150°
ANSWER
The sine is positive, the cosine is negative, and the
tangent is negative.
14.
225°
ANSWER
The sine is negative, the cosine is negative, and the
tangent is positive.

24. VOLLEYBALL players spike the ball at speeds up to 100 miles per hour to prevent the opponent from being able to return the ball.

26. Slip