Domanda del libro di testo
Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 5
In Exercises 5–7, convert each angle in radians to degrees. 5𝜋 3
Guida verificata passo dopo passo1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Identify the given angle in radians: \(\frac{5\pi}{3}\).
Substitute the given angle into the conversion formula: \(\frac{5\pi}{3} \times \frac{180}{\pi}\).
Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{5 \times 180}{3}\).
Perform the division and multiplication to find the angle in degrees.
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Radian Measure
A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. Radians provide a natural way to measure angles in terms of the circle's geometry, and many trigonometric functions use radians as their standard input.
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5:04
Converting between Degrees & Radians
Degree Measure
Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation. Degrees are often used in practical applications and are related to radians through a fixed conversion factor.
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5:04Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the fact that π radians equal 180 degrees. For example, converting 5π/3 radians to degrees involves multiplying 5π/3 by 180/π, simplifying to 300 degrees.
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5:04Converting between Degrees & Radians
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Find the reference angle for 16𝜋 3
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In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.
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In Exercises 5–7, convert each angle in radians to degrees. 7𝜋 5
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The unit circle has been divided into twelve equal arcs, corresponding to t-values of
0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<IMAGE>
sin 𝜋/6
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In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋
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