Pre-Calc Chapter 5 Test Review

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Questions and Answers

Convert the angle from degrees to radians. Express the answer as a multiple of π. What is the result for 324 degrees?

9π / 5

Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(√3 / 2)?

π / 6

Given the point (-3, -4), find the values of the six trigonometric functions of Θ.

sinΘ = -4/5, cscΘ = -5/4, cosΘ = -3/5, secΘ = -5/3, tanΘ = 4/3, cotΘ = 3/4

Use the given trigonometric function value of Θ to find the exact value of the remaining five trigonometric functions. If cotΘ = 1/3, what are the remaining functions?

sinΘ = 3√10 / 10, cscΘ = √10 / 3, cosΘ = √10 / 10, secΘ = √10, tanΘ = 3 Signup and view all the answers

Use the reference angle to find the exact value of the expression. What is sin(945 degrees)?

-√2 / 2 Signup and view all the answers

Graph the function over a one-period interval. For y = 4csc(2x), what are the key points?

(0, 0), (π/4, 4), (π/2, 0), (3π/4, -4), (π, 0) Signup and view all the answers

Convert the angle from radians to degrees. What is the result for -11π/10?

-198 degrees Signup and view all the answers

Convert the angle to decimal degree notation. What is 17 degrees 28 minutes 33 seconds in decimal degrees?

17.48 degrees Signup and view all the answers

Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(-2)?

Undefined Signup and view all the answers

Convert the angle to DMS notation. What is the result for 29.27 degrees?

29°16'12" Signup and view all the answers

Find the amplitude, period, and phase shift of the function y = 4cos(x - π/4).

Amplitude: 4, Period: 2π, Phase Shift: π/4 Signup and view all the answers

Find the exact values of the remaining trigonometric functions of Θ from the given information. If tanΘ = -3/4 and Θ is in quadrant II, what are the values?

sinΘ = 3/5, cscΘ = 5/3, cosΘ = -4/5, secΘ = -5/4, tanΘ = -3/4, cotΘ = -4/3 Signup and view all the answers

Graph the function over a one-period interval for y = 2tan(4x). What is the vertical shift and period?

Vertical Shift: 0, Period: π/4 Signup and view all the answers

Find the exact values of the remaining trigonometric functions of Θ from the given information. If secΘ = -5/3 and tanΘ > 0, what are the values?

sinΘ = -4/5, cscΘ = -5/4, cosΘ = -3/5, secΘ = -5/3, tanΘ = 4/3, cotΘ = 3/4 Signup and view all the answers

Find the remaining sides and angles of the triangle ABC, with right angle at C. If A = 63 degrees and c = 15, what are the lengths of the remaining sides?

6.8 and 13.4 Signup and view all the answers

Find the amplitude, period, and phase shift of the function y = -3sin(2x).

Amplitude: 3, Period: π, Phase Shift: none Signup and view all the answers

Use a sketch to find the exact value of y or explain why it is undefined for y = cot(sin^(-1)(3/5)). What is y?

4/3 Signup and view all the answers

Study Notes

Angle Conversion

Convert 324° to radians: Result is ( \frac{9\pi}{5} ).
Convert -(\frac{11\pi}{10}) radians to degrees: Result is -198°.
Convert 17°28'33" to decimal degree notation: Result is 17.48°.
Convert 29.27° to DMS notation: Result is 29°16'12".

Trigonometric Values and Functions

Exact value for ( y = \cos^{-1}(\frac{\sqrt{3}}{2}) ): Result is ( \frac{\pi}{6} ).
Value for ( y = \cos^{-1}(-2) ): Undefined since -2 is outside the function's domain.
Determine trigonometric functions for the point (-3, -4):
- ( \sin \Theta = -\frac{4}{5} ), ( \cos \Theta = -\frac{3}{5} )
- ( \tan \Theta = \frac{4}{3} ), and corresponding cosecant, secant, cotangent values.
For ( \cot \Theta = \frac{1}{3} ):
- ( \sin \Theta = \frac{3 \sqrt{10}}{10} ), ( \cos \Theta = \frac{\sqrt{10}}{10} )
- Full set of trigonometric functions can be derived.

Graphing Functions

Graph ( y = 4\csc(2x) ) with key points: (0, 0), ( \left(\frac{\pi}{4}, 4\right) ), ( \left(\frac{\pi}{2}, 0\right) ), ( \left(\frac{3\pi}{4}, -4\right) ), (π, 0).
Graph ( y = 2\tan(4x) ) with vertical asymptotes at -(\frac{\pi}{8}) and (\frac{\pi}{8}).
For ( y = 4\cos(x - \frac{\pi}{4}) ):
- Amplitude: 4, Period: ( 2\pi ), Phase Shift: ( \frac{\pi}{4} )
- Key points: ( \left(\frac{\pi}{4}, 4\right) ), ( \left(\frac{3\pi}{4}, 0\right) ), etc.

Triangle and Angle Calculations

For triangle ABC with ( A = 63° ), ( c = 15 ): Remaining sides approximately 6.8 and 13.4.
Explore functions with known values:
- For ( \tan \Theta = -\frac{3}{4} ) in quadrant II:
  - ( \sin \Theta = \frac{3}{5} ), ( \cos \Theta = -\frac{4}{5} )
- For ( \sec \Theta = -\frac{5}{3} ) with ( \tan \Theta > 0 ):
  - ( \sin \Theta = -\frac{4}{5} ), ( \cos \Theta = -\frac{3}{5} )

Additional Trigonometric Evaluations

Evaluate ( y = \cot(\sin^{-1} \frac{3}{5}) ): Result is ( \frac{4}{3} ).

Function Characteristics

For ( y = -3\sin(2x) ):
- Amplitude: 3, Period: ( \pi ), Phase Shift: None.

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Prepare for your Pre-Calculus Chapter 5 test with these flashcards that cover converting angles from degrees to radians, finding exact values of inverse trigonometric functions, and determining the values of trigonometric functions based on given points. This comprehensive review will help solidify your understanding of key concepts in trigonometry.