Assertion: trigonometric function's value | /r/HasProperty | necessary
Facets:
Source sentences:
text: (The absolute value in the expression is necessary as the product of secant and tangent in the interval of y is always nonnegative, while the radical x 2 − 1 {\displaystyle {\sqrt {x^{2}-1}}} is always nonnegative by definition of the principal square root, so the remaining factor must also be nonnegative, which is achieved by using the absolute value of x.)
text: One option is to call the library routines once, to build up a table of those trigonometric values that will be needed, but this requires significant memory to store the table.
text: (The absolute value in the expression is necessary as the product of cosecant and cotangent in the interval of y is always nonnegative, while the radical x 2 − 1 {\displaystyle {\sqrt {x^{2}-1}}} is always nonnegative by definition of the principal square root, so the remaining factor must also be nonnegative, which is achieved by using the absolute value of x.)