Name: ______________________________ Section: ______
Scholars’ Academy Precalculus
Unit 9: Analytical Trigonometry
Topic 1: Learning Target Checklist (Check the box if learning target was meet)
● I can determine the properties of inverse trigonometric functions.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
1) How can we determine the domain and range of trigonometric functions such as sine, cosine, and tangent?
2) Explain the relationship between the inverted functions versus the original trigonometric functions.
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Do Now:
TOPIC 1 TASK CARD
Inverse Trigonometric Functions
TASK A
TASK B
TASK C
Topic 2: Learning Target Checklist (Check the box if learning target was meet)
● I can solve basic trigonometric equations by modeling with mathematics.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
3) Why is it important to understand the relationship between angle and its reference angle?
4) Why is it important to determine the quadrants in which the terminal ray of the solution lies?
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Do Now:
TOPIC 2 TASK CARD
Solving Trigonometric Equations
TASK A
TASK B
TASK C
Topic 3: Learning Target Checklist (Check the box if learning target was meet)
● I can determine the value of sine and cosine by using the pythagorean and sum & difference identities.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
5) How can we use trigonometric identities to solve trigonometric expressions?
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Do Now:
TOPIC 3 TASK CARD
The Pythagorean and Sum & Difference Identities
TASK A
TASK B
5. The angle θ has its terminal ray in the second quadrant and sinθ = 5/13 . Algebraically determine the
value of cosθ .
6. The angle θ has its terminal ray in the third quadrant and cosθ = 8/10 . Algebraically determine the
value of sinθ .
TASK C
7.
8.
Name: ______________________________ Section: ______
Topic 4: Learning Target Checklist (Check the box if learning target was meet)
● I can determine the value of sine and cosine by using double angle identities.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
6) How can we use trigonometric identities to solve trigonometric expressions?
7) How do I know which identity to use when solving trigonometric equations?
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Do Now:
TOPIC 4 TASK CARD
Double Angle Identities
TASK A
TASK B
TASK C
Topic 5: Learning Target Checklist (Check the box if learning target was meet)
● I can solve trigonometric equations by modeling with mathematics.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
8) How can we use trigonometric identities to solve trigonometric expressions?
9) How do I know which identity to use when solving trigonometric equations?
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Do Now:
Which of the following is equivalent to cos(100°)cos(20°)+sin(100°)sin(20°)?
a. cos(120°) b. sin(120°)
c. cos(80°) d. sin(80°)
Think Share Critique:
Solve the equation for all values on the interval
TOPIC 5 TASK CARD
Solving Trigonometric Equations Day 1
TASK A
TASK B
TASK C
Topic 6: Learning Target Checklist (Check the box if learning target was meet)
● I can solve trigonometric equations by modeling with mathematics.
It’s Self-Assess Time: Circle the number that best describes how you feel about this lesson
5 - Good to go! 4 3 - Taking it slow. 2 1 - Need directions.
Reflection:
10) How can we use trigonometric identities to solve trigonometric expressions?
11) How do I know which identity to use when solving trigonometric equations?
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Do Now:
Create an equivalent trigonometric expression to the following: .
Identify and explain the trigonometric identities or algebraic properties used in each step of your
simplification.
Think - Share - Critique
Choose one of the following to prove:
Hint: Use the unit circle or a right triangle or trigonometric identities.
a. Prove the identity b. Prove the identity
= 1.
TOPIC 6 TASK CARD
Solving Trigonometric Equations Day 2
TASK A
1. Which of the following represents the largest solution, on the interval of the trigonometric equation to
the nearest degree?
a. 215° b. 341°
c. 325° d. 285°
2. Determine the solution set of on the interval [0°, 360°]
a. {45°, 135°} b. {30°, 150°}
c. {30°, 330°} d. {60°, 240°}
3. Which of the following sets represents all solutions to on the interval [0°, 360°)?
a. {0°, 180°, 270°} b. {90°, 270°}
c. {0°, 90°, 270°} d. {90°, 360°}
4. The smallest solution to on the interval is
a. 60° b. 15°
c. 30° d. 90°
TASK B
1. Algebraically solve the following trigonometric equations for all values of x within the interval [0, 2].
2. Graphically solve the following trigonometric equations for all values of x within the interval [0°, 360°].
Round all non integer answers to the nearest tenth of a degree, In each case, provide a graph that justifies
your solution. Include the equation of any curves sketched, the window you used, and any intersections
or intercepts needed for the solution. Don’t forget to state the solution set.
a. b.
Task C
At an amusement park, two different rides are operating near each other, and their vertical movements
over time are being studied to synchronize their peak moments for a cool visual effect.
Ride A: A wave-swinger-style ride that moves up and down in a more complex pattern, where
the vertical height in meters is and is the time in seconds is modeled by the equation:
Ride B: A traditional carousel that also rises and falls slightly as it rotates, where the vertical
height in meters is modeled by the equation:
Graphically find the times when the vertical positions of both rides are synchronized. Solve for all values
of x in the interval . Round your final answers to the nearest tenth of a degree.
