Domanda del libro di testo
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
9.84763
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 62
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.7826
Guida verificata passo dopo passo1
Identify the problem: We need to find the value of \( s \) in the interval \( [0, \frac{\pi}{2}] \) such that \( \cos s = 0.7826 \).
Recall the inverse cosine function: To find \( s \), we use the inverse cosine (arccos) function, which gives \( s = \arccos(0.7826) \).
Apply the inverse cosine: Use a calculator or a computational tool to find \( s = \arccos(0.7826) \). Make sure your calculator is set to radians since the interval is given in radians.
Round the result: After calculating \( s \), round the value to four decimal places as requested.
Verify the solution: Check that the value of \( s \) lies within the interval \( [0, \frac{\pi}{2}] \) and that \( \cos s \) is approximately 0.7826 to confirm correctness.
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Concetti chiave
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Inverse Trigonometric Functions
Inverse trigonometric functions allow us to find the angle when the value of a trigonometric ratio is known. For example, to find s such that cos s = 0.7826, we use the arccos (cos⁻¹) function, which returns the angle whose cosine is 0.7826.
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Percorso guidato
4:28
Introduction to Inverse Trig Functions
Domain and Range of Cosine and Arccosine
The cosine function outputs values between -1 and 1 for angles in radians. Its inverse, arccos, returns angles in the range [0, π]. Since the problem restricts s to [0, π/2], the solution must lie within this interval, ensuring the angle corresponds to the first quadrant.
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Percorso guidato
4:22Domain and Range of Function Transformations
Rounding and Approximation
When calculating trigonometric values, results often need to be rounded to a specified number of decimal places. Here, the angle s must be approximated to four decimal places, which requires careful use of a calculator or software to ensure precision and accuracy.
Video consigliato:
Percorso guidato
4:45How to Use a Calculator for Trig Functions
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