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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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 58
Give the exact value of each expression. See Example 5. cot 45°
Guida verificata passo dopo passo1
Recall the definition of cotangent in terms of sine and cosine: \(\cot \theta = \frac{\cos \theta}{\sin \theta}\).
Substitute \(\theta = 45^\circ\) into the formula: \(\cot 45^\circ = \frac{\cos 45^\circ}{\sin 45^\circ}\).
Use the known exact values for sine and cosine at \(45^\circ\): \(\sin 45^\circ = \frac{\sqrt{2}}{2}\) and \(\cos 45^\circ = \frac{\sqrt{2}}{2}\).
Replace the sine and cosine values in the expression: \(\cot 45^\circ = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}\).
Simplify the fraction by dividing the numerator by the denominator to find the exact value of \(\cot 45^\circ\).
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Definition of Cotangent
Cotangent is a trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle, or equivalently, cot(θ) = 1 / tan(θ). It represents the reciprocal of the tangent function and is useful for finding exact values of angles.
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Percorso guidato
5:37
Introduction to Cotangent Graph
Exact Values of Common Angles
Certain angles like 30°, 45°, and 60° have well-known exact trigonometric values. For 45°, the cotangent value can be derived from the properties of an isosceles right triangle, where the legs are equal, leading to cot 45° = 1.
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Percorso guidato
3:47Introduction to Common Polar Equations
Using Reciprocal Identities
Reciprocal identities relate trigonometric functions to their reciprocals, such as cot(θ) = 1 / tan(θ). This identity allows calculation of cotangent values by first knowing or finding the tangent value, simplifying the process of finding exact trigonometric values.
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04:42Solve Trig Equations Using Identity Substitutions
Pratica correlata
Domanda del libro di testo
Solve each problem.See Examples 3 and 4. Angle of Elevation of the Sun The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun to the nearest hundredth of a degree.
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Domanda del libro di testo
Determine whether each statement is true or false. If false, tell why. See Example 4. tan² 60° + 1 = sec² 60°
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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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Domanda del libro di testo
Determine whether each statement is true or false. If false, tell why. See Example 4. cos 60° = 2 cos² 30° - 1
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Domanda del libro di testo
Give the exact value of each expression. See Example 5. sec 45°
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