12.4.1b Coterminal Angles

Angles in standard position use the positive side of the x-axis as the inital arm.  Counter-clockwise rotations from this initial arm produce positive angles, and clockwise rotations produce negative angles.  Sometimes, different angles can end up with the same terminal arm.  These are called coterminal angles.

Resources:

• Notes

Assignment:

• p175 #7-9, 11, 18-20 C5

Things you should know how to do after today:

• define an angle in standard position
• define a coterminal angle
• Find the reference angle for an angle in standard position
• Find the smallest positive coterminal angle for any angle in standard position

Attachments:

File	Description	File size
12.4.1b.notes.pdf		412 kB

12.4.2a The Unit Circle

The foundation for a lot of trigonometry is the unit circle.

Resources

• Notes

Assignment

• p187 #1-4, 10, 11

Things you should be able to do after today:

• recall the relationship between radian measure with the number of radiuses around the circumference of a circle
• using special triangles, determine the coordinates for a point on the terminal arm when given the measure of the a standard position angle in radians

Attachments:

File	Description	File size
12.4.2a.notes.pdf		910 kB

12.4.2b Unit Circle

Resources

• Notes

Assignment

• p187 #5, 6, 7, 9, 12, 13, 15, C1 C2 *17 *18

Things you should be able to do after today:

• Given the coordinates of a point on the unit circle, determine the measure of the standard position angle in radians

Attachments:

File	Description	File size
12.4.2b.notes.pdf		618 kB

12.4.3a Trigonometric Ratios

Resources

• Notes

Assignment

• Example 2, DEF from the the notes will be marked next class
• p201 #1-9, 13, 14, 17, 18 C3

Things you should be able to do after today:

• Given an angle in standard position, determine:
  • sinθ, cosθ, tanθ, secθ, cscθ and cotθ

Attachments:

File	Description	File size
12.4.3a.notes.pdf		509 kB

12.4.3b Finding the Arc Length

Resources

• Notes: 12.4.3b

Assignment

• p201 #10, 11, 12, 15, 16, C1, C2 *20,22, 24

Attachments:

File	Description	File size
12.4.3b.notes.pdf		458 kB

12.4.4 Solving Trigonometric Equations

Resources

• Notes: Introduction to solving trigonometric equations
  • Notes: 4.4a
  • Notes: 4.4b

Assignment

• p211 #1, 3, 5, 6, 10, 11, 15, 16

Things you should be able to do after today:

• solve an equation involving trigonometric functions for:
  • specific domains
  • general solutions (solved over the reals)

Attachments:

File	Description	File size
12.4.4a.notes.pdf		430 kB
12.4.4b.notes.pdf		433 kB

12.4.5 Review

Warmup Answer Key:

1.

 2.