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Use the unit circle shown to find the value of the trigonometric function.
sin (2𝜋/3)
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 2
In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 15°
Guida verificata passo dopo passo1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given angle in degrees (15°) into the formula: \(15 \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{15}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 15.
After simplification, express the result as a multiple of \(\pi\) in the form \(\frac{1}{12} \pi\).
Write the final answer as \(\frac{\pi}{12}\) radians.
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Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many trigonometric applications.
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Percorso guidato
5:04
Converting between Degrees & Radians
Understanding π as a Constant
π (pi) is an irrational constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. Expressing angles as multiples of π provides a precise and standardized way to represent radian measures.
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Percorso guidato
6:02Stretches and Shrinks of Functions
Simplifying Radicals and Fractions
After converting degrees to radians, the result should be simplified as a fraction multiplied by π. Simplifying fractions ensures the answer is in its simplest form, making it easier to interpret and use in further calculations.
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Percorso guidato
4:02Solving Linear Equations with Fractions
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