Domanda del libro di testo
Use a calculator to approximate each value in decimal degrees.
θ = cot⁻¹ (-0.60724226)
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Ch. 6 - Inverse Circular Functions and Trigonometric Equations
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
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Lial 12th EditionCh. 6 - Inverse Circular Functions and Trigonometric EquationsProblema 53
Lial 12th EditionCh. 6 - Inverse Circular Functions and Trigonometric EquationsProblema 53Capitolo 7, Problema 53
Use a calculator to approximate each value in decimal degrees.
θ = csc⁻¹ 1.9422833
Guida verificata passo dopo passo1
Recall that the cosecant function is the reciprocal of the sine function, so \( \csc \theta = x \) implies \( \sin \theta = \frac{1}{x} \).
Rewrite the given expression \( \theta = \csc^{-1} 1.9422833 \) as \( \theta = \sin^{-1} \left( \frac{1}{1.9422833} \right) \).
Calculate the reciprocal of 1.9422833 to find \( \sin \theta \), which is \( \frac{1}{1.9422833} \).
Use a calculator to find the inverse sine (arcsin) of the value obtained in the previous step, making sure your calculator is set to degree mode.
The result from the calculator will give you the approximate value of \( \theta \) in decimal degrees.
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Inverse Cosecant Function (csc⁻¹)
The inverse cosecant function, csc⁻¹(x), returns the angle whose cosecant is x. Since cosecant is the reciprocal of sine, csc⁻¹(x) = sin⁻¹(1/x). Understanding this relationship helps convert the problem into a more familiar inverse sine calculation.
Video consigliato:
Percorso guidato
6:22
Graphs of Secant and Cosecant Functions
Reciprocal Trigonometric Functions
Cosecant is the reciprocal of sine, meaning csc(θ) = 1/sin(θ). This reciprocal relationship is essential for rewriting the inverse cosecant expression in terms of inverse sine, which is commonly available on calculators.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Using a Calculator to Find Angles in Degrees
Calculators typically provide inverse sine functions and allow switching between radians and degrees. To approximate θ in decimal degrees, convert csc⁻¹(x) to sin⁻¹(1/x) and ensure the calculator is set to degree mode before computing the angle.
Video consigliato:
Percorso guidato
4:45How to Use a Calculator for Trig Functions
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Use a calculator to approximate each value in decimal degrees.
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