The sine of 240 is the negative of sine 60, while the cosine is the negative of cosine 60. Regardless of the quadrant, this angle is always positive and less than 90 degrees.
240 Degrees Reference Angle Math: Finding the Acute Angle in the Third Quadrant
The calculation is straightforward: 240 minus 180 results in 60 degrees. The process involves subtracting 180 degrees from the initial measurement to find the acute counterpart.
Function Reference Angle (60°) Value at 240° Sine √3/2 -√3/2 Cosine 1/2 -1/2 Tangent √3 √3 Practical Application Mastering this concept allows for the quick evaluation of expressions involving angles beyond the standard 0 to 90-degree range. This specific angle lies between 180 and 270 degrees, placing it where both sine and cosine values are negative.
Calculating the 240 Degrees Reference Angle
Trigonometric Values Using the reference angle of 60 degrees, we can determine the exact trigonometric ratios for 240 degrees. Therefore, the acute reference value is 60 degrees, which corresponds to the known values of the equilateral triangle.
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