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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?
Convert the angle from degrees to radians. Express the answer as a multiple of π. What is the result for 324 degrees?
9Ï€ / 5
Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(√3 / 2)?
Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(√3 / 2)?
Ï€ / 6
Given the point (-3, -4), find the values of the six trigonometric functions of Θ.
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?
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?
Use the reference angle to find the exact value of the expression. What is sin(945 degrees)?
Use the reference angle to find the exact value of the expression. What is sin(945 degrees)?
Graph the function over a one-period interval. For y = 4csc(2x), what are the key points?
Graph the function over a one-period interval. For y = 4csc(2x), what are the key points?
Convert the angle from radians to degrees. What is the result for -11Ï€/10?
Convert the angle from radians to degrees. What is the result for -11Ï€/10?
Convert the angle to decimal degree notation. What is 17 degrees 28 minutes 33 seconds in decimal degrees?
Convert the angle to decimal degree notation. What is 17 degrees 28 minutes 33 seconds in decimal degrees?
Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(-2)?
Find the exact value of y or state why it is undefined. What is y for y = cos^(-1)(-2)?
Convert the angle to DMS notation. What is the result for 29.27 degrees?
Convert the angle to DMS notation. What is the result for 29.27 degrees?
Find the amplitude, period, and phase shift of the function y = 4cos(x - π/4).
Find the amplitude, period, and phase shift of the function y = 4cos(x - π/4).
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?
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?
Graph the function over a one-period interval for y = 2tan(4x). What is the vertical shift and period?
Graph the function over a one-period interval for y = 2tan(4x). What is the vertical shift and period?
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?
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?
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?
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?
Find the amplitude, period, and phase shift of the function y = -3sin(2x).
Find the amplitude, period, and phase shift of the function y = -3sin(2x).
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?
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?
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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) ), (Ï€, 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} )
- For ( \tan \Theta = -\frac{3}{4} ) in quadrant II:
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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