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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 � .