Final answer:
The exact value of csc(225°) is found by taking the reciprocal of sin(225°), which is -√2/2. After rationalizing the denominator, the answer is -√2.
Step-by-step explanation:
The question asks for the exact value of csc(225°). First, recognize that csc(θ) = 1/sin(θ). Thus, csc(225°) is the reciprocal of sin(225°).225° is in the third quadrant where sine is negative.
The reference angle for 225° is 45°, and the sine of 45° is √2/2. Therefore, sin(225°) = -√2/2. Taking the reciprocal of this, we get csc(225°) = -2/√2. Rationalizing the denominator, multiply both the numerator and the denominator by √2 to obtain csc(225°) = -√2.
To solve for the exact value of csc 225, we need to find the reciprocal of the sine of 225 degrees. Since the sine of 225 degrees is equal to -1/√2, the reciprocal of -1/√2 is -√2. Therefore, the exact value of csc 225 is -√2.
Thus, the correct answer is a) csc 225 = -√2.