-1-

Write each positive angle in degrees for each terminal side between 0° and 360°

NAME ____________________________________

Standard Position Initial Side Terminal Side Coterminal Angles

Positive Angles Negative Angles

-2-

Draw each angle in standard form. Determine the quadrant in which the terminal side lies. 190° 1° 300° 405° -90° 135° -330° 179° -60°

-3-

Write each positive angle in RADIANS for each terminal side between 0 and 2π

MEASURING ANGLES IN RADIANS

When a measurement of an angle is given with no units, the angle is measured in radians

Draw an angle measuring 6.28 radians

Draw an angle measure of 5

-4-

Put all the information together on one circle Label each terminal side in degrees. Label each terminal side in radians.

-5-

-6-

Trigonometric Functions in Right Triangles

Special Right Triangles Complete the following using the triangles above:

sin

cos

tan

θ

θ

θ

=

=

=

csc

sec

cot

θ

θ

θ

=

=

=

sin 45

cos45

tan45

csc45

sec45

cot45

° =

° =

° =

° =

° =

° =

sin30

cos30

tan30

csc30

sec30

cot30

° =

° =

° =

° =

° =

° =

sin60

cos60

tan60

csc60

sec60

cot60

° =

° =

° =

° =

° =

° =

-7-

Write the angle measurements in RADIANS. Then fill in the lengths of the sides. Complete the following using the triangles above: Find the value of ANY trig ratio by drawing a triangle with the hypotenuse as the terminal side of the given angle.

sin4

cos4

tan4

csc4

sec4

cot4

π

π

π

π

π

π

=

=

=

=

=

=

sin3

cos3

tan3

csc3

sec3

cot3

π

π

π

π

π

π

=

=

=

=

=

=

sin6

cos6

tan6

csc6

sec6

cot6

π

π

π

π

π

π

=

=

=

=

=

=

-8-

Find the exact value of each trigonometric ratio. Draw a triangle to help you determine the ratio. Leave answers in simplified radical form.

1. cos4π=

2. cos3π= 3. sec

3π=

4. sin6=

π

5. tan4π=

6. cos6π= 7. sec

6=

π 8. tan

6=

π

9. cos6=

π

10. csc4=

π 11. tan

3π= 12. sec

6=

π

13. cot6=

π

14. sin3=

π 15. cot

4=

π 16. csc

3=

π

17. tan6π=

18. sec6π= 19. cos

6=

π

20. tan3=

π

21. cos4=

π

22. csc6=

π 23. sec

4=

π 24. cot

3π=

25. sin4π=

26. sec3=

π 27. sin

3π= 28. tan

3π=

-9-

Reference Angles –

Find 5cos4π

Find 5csc6π− Find 7tan

4π

Find 13cot6π Find 3sin

4π

Find sec3π− Find 2tan

3π

1. Draw the angle in standard position. 2. Create a triangle - draw a vertical line from the terminal side (hypotenuse) to the x-axis 3. Find the acute angle formed - it may be a part of the given angle or it may be outside of the given angle. This is called the reference angle 4. Write in the lengths of the sides based on the reference angle formed (use special right triangles) Hypotenuse - ALWAYS positive x or y side - may be positive or negative 5. Find the ratio - simplify if necessary.

-10-

Find the exact value of each trigonometric ratio. Draw a sketch of your angle, complete the reference triangle in the correct position, and label all sides of the triangle.

1. sin65π

= 2. csc 53π

=

3. cos 76π

= 4. tan 54π

=

5. cot 32π

= 6. cos 611π

=

7. sec 35π

= 8. sin 43π

=

9. tan 56π

= 10. cos 23π

=

11. sin 3π

= 12. cos 74π

=

13. csc 34π

= 14. sec 3π

=

-11-

Which trig ratios are positive in the first quadrant? Which trig ratios are positive in the second quadrant? Which trig ratios are positive in the third quadrant? Which trig ratios are positive in the fourth quadrant? Quadrantal Angles

-12-

Quadrantal Angles - Find the exact value of each trigonometric ratio. Draw the angle and mark the point on the terminal side.

1. sin 2π

= 2. cos 32π

=

3. tan π = 4. sec 2π

=

5. csc 32π= 6. cot π2 =

7. tan 2π= 8. sinπ =

9. cot 0 = 10. csc 2π

=

11. cos π = 12. sec 32π

=

13. cos2π

= 14. sin 23π

=

-13-

Review Reference Angles

1. cos4π=

2. cos3π= 3. sec

3π=

4. tan4π= 5.

5sin3π=

6. sin2π=

7. cos6π= 8.

5sec6π= 9. sin

6π=

10. cosπ =

11. 7

cos6π=

12. 7csc4π= 13. tan

3π= 14.

7sec6π= 15.

7sin4π=

16. 7tan6π=

17. 2

cos3π= 18.

3sec2π−= 19.

5csc3π= 20.

3cot

4π=

21. tan6π=

22. sec6π= 23. sin

32π

=

24. 2tan3π= 25.

5cos

6π=

26. 5

cos4π=

27. tanπ = 28. sec

2π−

= 29. cot3π= 30.

11csc6π=

31. sin4π=

32. 3

cot2π−= 33. sin

3π=

34. sin 2π = 35. tan

3π=

-14-

Find the exact value of the following trigonometric ratios.

-15-

-16-

Given a point or a ratio, find all trig values!

-17-

-18-

Quadrant Restrictions

-19-

For the following problems, determine in which quadrant the angle must lie. Then find the other trigonometric ratio.

1. Given: sin θ = 41

− and cos θ > 0. Find tanθ .

2. Given: tan θ = 43

and sin θ < 0. Find cosθ .

3. Given: cos θ = 43

and sin θ > 0. Find cscθ .

4. Given: tan θ = -125

and sin θ > 0. Find cosθ .

5. Given: sec θ = -3 and tan θ > 0. Find cotθ . 6. Given: csc θ = 2 and tan θ < 0. Find cosθ .

-20-

For the following problems, a point on the terminal side of angleθ is given. Find the exact value of the other trig ratio. 7. (-4, 3); cosθ 8. (-2, -5); tanθ 9. ( )2,2 − ; sinθ Find the exact value of each trigonometric function or find θ in the interval πθ 20 ≤≤ .

10. 7sin4π= 12. 3cos

2θ = −

13. 5cot3π= 14. csc2π =

15. tanθ = undefined 16. 7cos6π=

17. 4sin3π= 18. 3sec

4π=

19. tan 1θ = ± 20. 11sin6π=

21. 1sin2

θ = 22. 1cos2

θ = −

-21-