Mastering Trigonometry: A PreCalculus Test Review

PreAlgebra Grades High School 31:13 Video
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Lesson Description

Ace your PreCalculus trigonometry test with this comprehensive review! We'll cover unit circle evaluation, trigonometric functions, graphing, and more. Pause, practice, and perfect your skills.

Video Resource

Trigonometry Test Review for PreCalculus Students (25 Questions)

Mario's Math Tutoring

Duration: 31:13
Watch on YouTube

Key Concepts

  • Unit Circle Evaluation
  • Trigonometric Functions of Angles
  • Graphing Trigonometric Functions and Transformations
  • Inverse Trigonometric Functions

Learning Objectives

  • Evaluate trigonometric functions using the unit circle without a calculator.
  • Determine all six trigonometric functions for a given angle.
  • Solve right triangles using trigonometric ratios.
  • Graph trigonometric functions and their transformations, identifying key features such as amplitude, period, phase shift, and vertical shift.
  • Evaluate inverse trigonometric functions.
  • Write equations for trig functions given certain characteristics.

Educator Instructions

  • Introduction (5 mins)
    Briefly introduce the importance of trigonometry in PreCalculus and real-world applications. Highlight the format of the video – a test review with problem-solving demonstrations.
  • Unit Circle and Angle Evaluation (15 mins)
    Review evaluating trigonometric functions (cosecant, cosine, tangent) for given angles (11π/6, 2π/3, 7π/4) using the unit circle. Emphasize the importance of reference angles and quadrant signs.
  • Trigonometric Functions of Right Triangles (10 mins)
    Discuss finding all six trigonometric functions given a right triangle. Review SOH CAH TOA and Pythagorean triples. Cover solving right triangles given angle and side measurements.
  • Graphing Trigonometric Functions (20 mins)
    Explain how to graph sine, cosine, tangent, cotangent, secant, and cosecant functions. Cover transformations such as amplitude, period, phase shift, and vertical shift. Break down domain and range.
  • Inverse Trigonometric Functions (10 mins)
    Demonstrate evaluating inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹). Emphasize the restricted domains of these functions.
  • Applications and Review (10 mins)
    Work through word problems involving trigonometry, such as the kite problem. Summarize key concepts and encourage further practice.

Interactive Exercises

  • Unit Circle Practice
    Students will be given a blank unit circle and asked to fill in the angles in radians and degrees, as well as the coordinates of key points. They will then use this to evaluate trigonometric functions for various angles.
  • Graphing Transformations
    Students will be given trigonometric function equations with various transformations and asked to sketch the graphs, labeling key features such as amplitude, period, phase shift, and vertical shift. They can use online graphing tools to check their answers.

Discussion Questions

  • How does understanding the unit circle simplify evaluating trigonometric functions?
  • What are the key transformations that affect the graph of a trigonometric function?
  • Why do inverse trigonometric functions have restricted domains?
  • In what real world scenarios might knowledge of trig functions be important?

Skills Developed

  • Unit Circle Proficiency
  • Trigonometric Function Evaluation
  • Graphing Trigonometric Functions
  • Problem-Solving
  • Analytical Thinking

Multiple Choice Questions

Question 1:

What is the exact value of cos(2π/3)?

Correct Answer: -1/2

Question 2:

If sin(θ) = 7/25, what is the value of csc(θ)?

Correct Answer: 25/7

Question 3:

What is the period of the function y = sin(2x)?

Correct Answer: π

Question 4:

Which quadrant does an angle of 7π/6 terminate in?

Correct Answer: Quadrant III

Question 5:

What is the range of the function y = 3cos(x) + 1?

Correct Answer: [-2, 4]

Question 6:

What is the phase shift of y = sin(x - π/2)?

Correct Answer: π/2 to the right

Question 7:

What is the exact value of sin⁻¹(-√2/2)?

Correct Answer: -π/4

Question 8:

What is a co-terminal angle of 7π/5

Correct Answer: 17π/5

Question 9:

What is the period of y = -2 csc(x-2)?

Correct Answer: 2π

Question 10:

Which trig function is positive in the second quadrant?

Correct Answer: Sine

Fill in the Blank Questions

Question 1:

The reciprocal of sine is _________.

Correct Answer: cosecant

Question 2:

The period of y = cos(x) is _________.

Correct Answer: 2π

Question 3:

The acronym SOH CAH TOA is used to remember the ratios of the _________ functions.

Correct Answer: trigonometric

Question 4:

An angle of 30 degrees is equal to _________ radians.

Correct Answer: π/6

Question 5:

The domain of y = sin⁻¹(x) is _________.

Correct Answer: [-1, 1]

Question 6:

A vertical stretch by a factor of 2, would change the _________ of the function.

Correct Answer: amplitude

Question 7:

If cosine is positive and cotangent is negative, the angle lies in quadrant _________.

Correct Answer: IV

Question 8:

y= a cos(Bx-H)+K: H is the _________ shift.

Correct Answer: phase

Question 9:

Tangent is equal to sine divided by _________.

Correct Answer: cosine

Question 10:

___________ is the inverse of the Tangent.

Correct Answer: arctan

Educational Standards

PC.T.1:Make sense of the unit circle and its relationship to the graphs of trigonometric functions. PC.T.1.2:Convert radian measure to degree measure and vice-versa. PC.T.1.8:Graph all six trigonometric functions, identifying key features. PC.T.2:Apply trigonometric concepts beyond the right triangle.

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