Domanda del libro di testo
In Exercises 31–34, determine the amplitude of each function. Then graph the function and y = cos x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 2 cos x
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Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblema 31
Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblema 31Capitolo 2, Problema 31
In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. cos⁻¹ 3/8
Guida verificata passo dopo passo1
Identify the expression to evaluate: \(\cos^{-1} \left( \frac{3}{8} \right)\), which means finding the angle whose cosine is \(\frac{3}{8}\).
Recall that the inverse cosine function, \(\cos^{-1}(x)\), returns an angle in radians or degrees depending on the calculator mode, typically between 0 and \(\pi\) radians (or 0° and 180°).
Make sure your calculator is set to the correct mode (degrees or radians) based on the problem's requirement. Since the problem does not specify, degrees is commonly used.
Use the calculator to compute \(\cos^{-1} \left( \frac{3}{8} \right)\) by entering the value \(0.375\) and then applying the inverse cosine function.
Round the resulting angle to two decimal places as requested.
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Inverse Cosine Function (cos⁻¹ or arccos)
The inverse cosine function returns the angle whose cosine value is a given number. It is used to find an angle when the cosine value is known, with the output typically in radians or degrees within the range 0 to π (0° to 180°).
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Percorso guidato
4:49
Inverse Cosine
Domain of the Cosine Function
The cosine function outputs values between -1 and 1, so its inverse function, arccos, only accepts inputs within this range. Any input outside [-1, 1] is invalid and will not produce a real angle.
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Percorso guidato
3:43Finding the Domain of an Equation
Using a Calculator for Trigonometric Functions
Calculators can compute inverse trigonometric functions, often requiring the mode to be set to degrees or radians. For cos⁻¹(3/8), input the fraction and use the inverse cosine function to find the angle, then round the result to two decimal places.
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Percorso guidato
4:45How to Use a Calculator for Trig Functions
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Graph two periods of the given cosecant or secant function.
y = 2 csc x
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In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 1/2 csc x/2
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Domanda del libro di testo
In Exercises 29–36, find the length x to the nearest whole unit.
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Domanda del libro di testo
In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ sin⁻¹ (− √3/2)
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Domanda del libro di testo
In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ (-0.32)
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