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 5.1.9
Use identities to correctly complete each sentence.
If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.
Guida verificata passo dopo passo1
Recall the identity for tangent of a negative angle: \(\tan(-\theta) = -\tan(\theta)\).
Calculate \(\tan(\theta)\) using the given values of sine and cosine: \(\tan(\theta) = \frac{\sin \theta}{\cos \theta}\).
Substitute the given values into the tangent formula: \(\tan(\theta) = \frac{0.6}{0.8}\).
Apply the negative angle identity to find \(\tan(-\theta)\): \(\tan(-\theta) = -\frac{0.6}{0.8}\).
Simplify the fraction if needed to express the final answer in simplest form.
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Trigonometric Ratios
Trigonometric ratios relate the angles of a right triangle to the ratios of its sides. The primary ratios are sine (sin), cosine (cos), and tangent (tan), where tan θ = sin θ / cos θ. Understanding these ratios is essential for calculating one function from others.
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Percorso guidato
6:04
Introduction to Trigonometric Functions
Even-Odd Identities
Even-odd identities describe how trigonometric functions behave with negative angles. Cosine is an even function, so cos(-θ) = cos θ, while sine and tangent are odd functions, meaning sin(-θ) = -sin θ and tan(-θ) = -tan θ. These identities help evaluate functions at negative angles.
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Percorso guidato
06:19Even and Odd Identities
Using Given Values to Find Tangent
Given values of sine and cosine allow direct calculation of tangent using tan θ = sin θ / cos θ. With sin θ = 0.6 and cos θ = 0.8, tan θ = 0.6 / 0.8 = 0.75. Applying the even-odd identity for tangent then gives tan(-θ) = -0.75.
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Percorso guidato
5:08Sine, Cosine, & Tangent of 30°, 45°, & 60°
Pratica correlata
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
725
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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.
cot α sin α
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Domanda del libro di testo
Find sinθ.
cot θ = -1/3, θ in quadrant IV
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Domanda del libro di testo
Verify that each equation is an identity.
sin² x(1 + cot x) + cos² x(1 - tan x) + cot² x = csc² x
787
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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)
709
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