9.4.6 Test (TST): Working with Trigonometric Functions Test
Precalculus Honors
Points Possible:100
Date: 04/29/2022
Answer the following questions using what you've learned from this unit. Write your responses
in
...
9.4.6 Test (TST): Working with Trigonometric Functions Test
Precalculus Honors
Points Possible:100
Date: 04/29/2022
Answer the following questions using what you've learned from this unit. Write your responses
in the space provided.
1. Sketch a graph of the function .
Part I: First, sketch at least two periods of the function on the graph below.
Part II: What are the domain and range of the function ?
range=[-1,1]
Part III: Restrict the domain of the function so that it may be inverted and draw
the reflection of this new graph of across the line y = x. This is a graph of the
function
2.
Part I: Evaluate the expression . Give the exact value ? answers expressed as
decimals will receive no credit.
Part II: Evaluate the expression . Give the exact value ? answers expressed
as decimals will receive no credit.
Part III: Evaluate the expression . Give the exact value ? answers expressed
as decimals will receive no credit.
Part IV: Evaluate the expression . Give the exact value ? answers expressed
as decimals will receive no credit.
3. Use a calculator to evaluate the expression. Round your answer to the nearest hundredth.
Part I:
Part II:
For questions 4 - 5, solve each equation on the interval .
4.
Part I: Find two values of that satisfy this equation.
Part II: Solve each equation separately to get the full solution set, choosing only
5.
Part I: Solve this equation for 3x, finding all values on the interval [0,2π] that satisfy the
equation.
Part II: Use algebra to find all values of x between 0 and 2π that satisfy this equation.
For questions 6 - 7, find all solutions to the equation.
6. .
Part I: Find the values of that satisfy the equation on the interval .
Part II: Write an expression for all solutions to the equation.
Part I: On the interval , what values of satisfy this equation?
Part II: On the interval , what values of does your answer to Part I produce?
(n)
Part III: Write an expression for all solutions to the equation
8. .
Part I: Factor this equation and solve for sinx.
9.
Part I: Solve each of the two equations in Part I for x, giving all solutions to the equation.
10. An object's motion is described by the equation . The displacement, , is
measured in meters. The time, , is measured in seconds.
Answer the following questions:
Part I: What is the object's position at ? Be sure to include appropriate units.
0 meters.
Part II: What is the object's maximum displacement from its resting position? Be sure to
include appropriate units.
4 meters
Part III: How much time is required for one oscillation? Be sure to include appropriate
units.
Part IV: What is the frequency of this motion? Be sure to include appropriate units.
Part V: What will the height of the object be at t = 1.75 seconds?
-2.83 meters
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