Domanda del libro di testo
Use a half-angle identity to find each exact value.
sin 195°
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Ch. 5 - Trigonometric Identities
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 6, Problema 5.34
Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
cot α sin α
Guida verificata passo dopo passo1
Recall the definition of cotangent: \( \cot \alpha = \frac{\cos \alpha}{\sin \alpha} \).
Substitute the definition of \( \cot \alpha \) into the expression: \( \cot \alpha \sin \alpha = \frac{\cos \alpha}{\sin \alpha} \cdot \sin \alpha \).
Observe that the \( \sin \alpha \) in the numerator and denominator cancel each other out.
Simplify the expression to \( \cos \alpha \).
Conclude that the expression simplifies to a single trigonometric function: \( \cos \alpha \).
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Concetti chiave
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Cotangent Function
The cotangent function, denoted as cot(α), is the reciprocal of the tangent function. It can be expressed as cot(α) = cos(α) / sin(α). Understanding cotangent is essential for simplifying expressions involving trigonometric functions, particularly when combined with sine or cosine.
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Percorso guidato
5:37
Introduction to Cotangent Graph
Sine Function
The sine function, sin(α), is a fundamental trigonometric function that relates the angle α to the ratio of the length of the opposite side to the hypotenuse in a right triangle. It is crucial for simplifying expressions that involve angles and is often used in conjunction with other trigonometric identities.
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Percorso guidato
5:53Graph of Sine and Cosine Function
Fundamental Trigonometric Identities
Fundamental trigonometric identities are equations that relate the various trigonometric functions to one another. These include identities such as sin²(α) + cos²(α) = 1 and the reciprocal identities. Utilizing these identities is key to simplifying trigonometric expressions effectively.
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Percorso guidato
5:32Fundamental Trigonometric Identities
Pratica correlata
Domanda del libro di testo
Use identities to correctly complete each sentence.
If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.
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Domanda del libro di testo
Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
1 - 1/sec² x
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Domanda del libro di testo
Verify that each equation is an identity.
sin² α + tan² α + cos² α = sec² α
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Domanda del libro di testo
Write each function as an expression involving functions of θ or x alone. See Example 2.
sin (3π/4 - x)
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Domanda del libro di testo
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
cot² θ(1 + tan² θ)
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