Trig Angle Chapter

Date Topic Assignment

1/20 Trig Angle Measures Worksheet #1

1/21 Trig Functions of General Angles Worksheet #2

1/22 Trig Functions of General Angles with Restrictions Worksheet #3

1/23 Special Right Triangles QUIZ

Worksheet #4

1/26 Trig Functions of General Angles with 30°, 45°, or 60° Reference Angles Worksheet #5

1/27 Trig Functions of General Angles with 30°, 45°, or 60° Reference Angles Worksheet #6

1/28 Trig Functions of General Angles with Non-30°, 45°, or 60° Reference Angles Worksheet #7

1/29 TRIG ANGLE REVIEW Review Packet

1/30 TRIG ANGLE CHAPTER TEST TBD

Advanced Algebra Trig Angle Chapter Day 1 – Angles

Learning Target: Students will be able to identify basic trig angles and be able to find coterminal angles.

Angle (from Geom): The union of two rays with a common endpoint (restricted to 0° < m < 180°). Trig Angles: An angle is formed by rotating a ray around its endpoint. Degree: A unit used to measure angles. 360° = 1 full rotation 180° = half of a rotation 90° = quarter of a rotation Acute Angle: Right Angle: Obtuse Angle: Straight Angle: Supplementary Angles: Complementary Angles: Standard Position:

Quadrantal Angles: Angles with the side on the x-axis or y-axis. Coterminal Angles: Angles with the same terminal side (i.e. 10 degrees and 370 degrees). Ex 1: Find the smallest positive coterminal angle with the given angle.

a) -98° b) 450° c) 800°

Find the measure of each angle.

Ex 2: Ex 3: Two angles are supplementary. If they measure (10x + 7)° and (7x + 3)°, then find the measure of each angle.

(4y)°

(2y)°

Advanced Algebra Angle Chapter Day 2 – SOH-CAH-TOA

Learning Target: Students will find all six trig functions when given a point and use quadrantals to evaluate expressions. Remember: SOH-CAH-TOA Place the ratios in SOH-CAH-TOA form and x, y, and r form.

sin cosecant = csc

cos secant = sec =

tan cotangent = cot

T T

T T

T T

Ex 1: Is xr

positive or negative in quadrant two? Ex 2: Is xr

positive or negative in quadrant four?

Ex 3: If the terminal side of D goes through � �8,15 , Ex 4: If the terminal side of D goes through � �5, 2� ,

then find all six trigonometric functions. then find all six trigonometric functions.

sin csc

cos sec =

tan cot

D D

D D

D D

sin csc

cos sec =

tan cot

D D

D D

D D

Ex 5: If the terminal side of T goes through � �3, 4� � , then find all six trigonometric functions.

sin csc

cos sec =

tan cot

T T

T T

T T

For quadrantal angles, use the following: SIN COS TAN Evaluate.

Ex 6: tan0 6sin90q� q Ex 7: 22sec0 4cot 90 cos360q� q� q

Advanced Algebra Angle Chapter Day 3 – Restrictions

Learning Target: Students will be able to find all six trig functions when restrictions are given. Restrictions on trigonometric functions – We will discuss this more when we graph!!

1 sin 1T� d d 1 cos 1T� d d csc 1or csc 1T Td � t sec 1or sec 1T Td � t

***tan & cot have NO restrictions*** Possible, or impossible?

a) 2 3 2csc , sin

3 2T T � � b)

3 4cos , sec4 3

T T c) sec 1 1.3T �

We can use a shortcut to decide which sign the trig ratios have in each quadrant. Determine which quadrant the given angle is located in.

Ex 1: sin 0T ! and cot 0T � Ex 2: csc 0T � and cos 0T � Calculate all six trigonometric ratios with the given information.

Ex 3: 2sin3

T and QIIT � Ex 4:

4tan3

T and sin 0T �

sin csc

cos sec =

tan cot

T T

T T

T T

sin csc

cos sec =

tan cot

T T

T T

T T

Ex 5: 3cos

4D � and sin 0.D !

sin csc

cos sec =

tan cot

D D

D D

D D

Advanced Algebra Angle Chapter Day 4 – Special Right Triangles

Learning Target: Students will be able to evaluate side of 30°-60°-90° and 45°-45°-90° triangles.

Write the ratios of the sides for the given triangles.

Find the missing sides for the given triangles.

Ex 1: Ex 2: Ex 3:

Ex 4: Ex 5: Ex 6:

30°

60°

45°

45°

60°

C

A

B

9 3

3

45°

C

B

A

30°

B

C A

26

15

60°

C

B

A

45° 12

B

C A

30°

B

C A 13

Find the following trig values.

sin30q = cos60q = tan30q= sin 60q= tan 45q= sin 45q= cos45q= cos30q=

Advanced Algebra Angle Chapter Day 5 – 30°-45°-60° Reference Angles

Learning Target: Students will be able to find a reference angle and all six trig functions for 30°, 60°, 45° angles.

Reference Angles: QI QII QIII QIV Find the reference angles

Ex 1: 218 32110' 1387 Remember from Geometry: Find all six trig functions for the angle given. Ex 2: 675 Ex 3: 240�

sin 675 csc675

cos675 sec675

tan 675 cot675

sin 240 csc 240

cos 240 sec 240

tan 240 cot 240

� �

� �

� �

30°

60°

45°

45°

Ex 4: 210

sin 210 csc 210

cos 210 sec 210

tan 210 cot210

Advanced Algebra Angle Chapter Day 6 – Find All Angle Measures

Learning Target: Students will be able to find a reference angle and finding angles given trig ratios.

Reference Angles: QI QII QIII QIV Remember: What does it mean? Remember: SOH-CAH-TOA What does it mean? Remember: [ vs. ) What does it mean?

A S

T C

30°

60°

45°

45°

Ex 1: Find all T in �0 ,360ª¬

if tan 3T . Ex 2: Find all T in �0 ,360ª¬

if 2cos

2T � .

(unrationalize)

Ex 3: Find all T in �0 ,360ª¬ if 3sin

2T � . Ex 4: Find all T in �0 ,360ª¬

if 3sec

3T .

Advanced Algebra Angle Chapter Day 7 – Non 30°, 45°, 60° Angles

Learning Target: Students will be able to find a reference angle and all six trig functions for non 30°, 45°, 60° angles. How do we find function values if they are not 30°, 60°, 45° reference angles? CALCULATOR!!!

(DEGREE MODE) Calculate each ratio using your calculator. (DEGREE MODE!)

Ex 1: sin130 48' sec97 58'37"

cos250 19' sin 246�

tan105.07 cot51.4283

Find T to the nearest minute.

Ex 2: sin 0.81815T cos 0.7352T sec 1.0545T cot 2.1365T

***CALCULATORS WILL ONLY GIVE YOU ONE OF THE TWO ANSWERS***

Here is the calculator order: QI Quadrantal Degrees QII (as big angle) QIV (as negative angle)

Ex 3: Find all T in �0 ,360ª¬

if cos 0.81416T . Ex 4: Find all T in �0 ,360ª¬ ifsin 0.5236T � .

Ex 5: Find all T in �0 ,360ª¬ if sec 4.5307T � .