Domanda del libro di testo
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3 cot θ = - —— 3
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Ch. 2 - Acute Angles and Right Triangles
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 3, Problema 64
Give the exact value of each expression. See Example 5. csc 60°
Guida verificata passo dopo passo1
Recall that the cosecant function is the reciprocal of the sine function, so \(\csc \theta = \frac{1}{\sin \theta}\).
Identify the angle given: \(60^\circ\).
Find the exact value of \(\sin 60^\circ\). From the special angles in trigonometry, \(\sin 60^\circ = \frac{\sqrt{3}}{2}\).
Use the reciprocal relationship to write \(\csc 60^\circ = \frac{1}{\sin 60^\circ} = \frac{1}{\frac{\sqrt{3}}{2}}\).
Simplify the expression by multiplying numerator and denominator appropriately to find the exact value of \(\csc 60^\circ\).
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Definition of Cosecant (csc)
Cosecant is the reciprocal of the sine function. For any angle θ, csc(θ) = 1/sin(θ). Understanding this relationship allows you to find the cosecant value by first determining the sine of the angle.
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Percorso guidato
6:22
Graphs of Secant and Cosecant Functions
Exact Values of Sine for Special Angles
Certain angles like 30°, 45°, and 60° have well-known exact sine values derived from special right triangles. For 60°, sin(60°) = √3/2, which is essential for calculating csc(60°) exactly.
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Percorso guidato
3:28Common Trig Functions For 45-45-90 Triangles
Reciprocal Function Calculation
To find the exact value of csc(60°), you take the reciprocal of sin(60°). This involves flipping the fraction representing sin(60°), turning √3/2 into 2/√3, which can be simplified further if needed.
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Percorso guidato
4:45How to Use a Calculator for Trig Functions
Pratica correlata
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Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. cos θ = √3 2
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Domanda del libro di testo
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Find a formula for h in terms of k, A, and B. Assume A < B.
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Concept Check Work each problem. Find the equation of the line that passes through the origin and makes a 30° angle with the x-axis.
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Domanda del libro di testo
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. sec θ = -√2
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Domanda del libro di testo
Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.
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