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Find the exact value of csc(−135°).

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Final answer:

The exact value of csc(-135°) is found by taking the reciprocal of sin(-135°). Since sin(-135°) is -√2/2, the cosecant of -135° is - √2.

Step-by-step explanation:

The question asks to find the exact value of csc(-135°), which is the cosecant of negative one hundred and thirty-five degrees. To find this value, first, recognize that cosecant is the reciprocal of the sine function. The sine of -135° can be found by referring to the unit circle or using trigonometric identities.

Sine of -135° is equivalent to sine of its reference angle 45° in the third quadrant, where sine is negative. Thus, sin(-135°) equals -sin(45°), which is -1/√2 or -√2/2. Finally, the cosecant of an angle is the inverse of its sine, so csc(-135°) = -1/sin(-135°) which simplifies to - √2.

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