Domanda del libro di testo
If θ is an acute angle and sin θ = (2√7) / 7, use the identity sin²θ + cos²θ = 1 to find cos θ.
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 27
In Exercises 21–28, convert each angle in radians to degrees. -3𝜋
Guida verificata passo dopo passo1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
Identify the given angle in radians, which is \(-3\pi\).
Substitute the given angle into the conversion formula: \(-3\pi \times \dfrac{180}{\pi}\).
Simplify the expression by canceling \(\pi\) in the numerator and denominator: \(-3 \times 180\).
Multiply the numbers to find the angle in degrees (do not calculate the final value here, just set up the expression).
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Radian Measure
Radian is a unit of angular measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It is a fundamental unit in trigonometry, where 2𝜋 radians equal 360 degrees.
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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 is further divided into 60 minutes and each minute into 60 seconds. Degrees are often used in practical applications and are related to radians by 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, to convert -3𝜋 radians, multiply -3𝜋 by 180/𝜋 to get -540 degrees.
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5:04Converting between Degrees & Radians
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