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Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. ―541°
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Ch. 1 - Trigonometric Functions
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 2, Problema 87
Use trigonometric function values of quadrantal angles to evaluate each expression. 3 sec 180° ― 5 tan 360°
Guida verificata passo dopo passo1
Recall the definitions and values of trigonometric functions at quadrantal angles: 180° and 360° are on the x-axis of the unit circle, where sine and cosine take specific values.
Evaluate \( \sec 180^\circ \). Since \( \sec \theta = \frac{1}{\cos \theta} \), first find \( \cos 180^\circ \), then take its reciprocal.
Evaluate \( \tan 360^\circ \). Recall that \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), so find \( \sin 360^\circ \) and \( \cos 360^\circ \) and compute their ratio.
Multiply the value of \( \sec 180^\circ \) by 3, and multiply the value of \( \tan 360^\circ \) by 5, as indicated in the expression.
Subtract the product \( 5 \tan 360^\circ \) from \( 3 \sec 180^\circ \) to get the final expression value.
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Quadrantal Angles
Quadrantal angles are angles that lie on the x- or y-axis in the coordinate plane, typically 0°, 90°, 180°, 270°, and 360°. Their trigonometric function values are special and often involve 0, ±1, or undefined values, which simplifies calculations.
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Percorso guidato
6:36
Quadratic Formula
Secant Function (sec θ)
The secant function is the reciprocal of the cosine function, defined as sec θ = 1/cos θ. Evaluating secant at quadrantal angles requires knowing the cosine values at those angles, which can be 0 or ±1, affecting whether secant is defined or undefined.
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Percorso guidato
6:22Graphs of Secant and Cosecant Functions
Tangent Function (tan θ)
The tangent function is the ratio of sine to cosine, tan θ = sin θ / cos θ. At quadrantal angles, tangent values can be 0, undefined, or ±1, depending on the sine and cosine values, which is crucial for correctly evaluating expressions involving tan 360°.
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Percorso guidato
5:43Introduction to Tangent Graph
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