Question

If 0=300 degrees, find the exact value of each expression below: (a) sin 0/2 (b) sin^2 0 (c) sin (-0)

Answer 1

To find the exact value of each expression: (a) sin(0/2) is approximately 0.866, (b) sin^2(0) is 0, and (c) sin(-0) is 0.

Step-by-step explanation:

To find the exact value of each expression:

(a) sin(0/2): Since 0 = 300 degrees, we can divide it by 2 to get 150 degrees. The sine of 150 degrees is √3/2 or approximately 0.866.

(b) sin²(0): The sine of 0 degrees is 0, so squaring it gives us 0.

(c) sin(-0): The sine of -0 degrees is still 0, so the exact value is 0.

Answer 2

The answer, assuming '0' is a typo for 'θ (theta)', involves finding sine values for 300 degrees: For (a) sin(θ/2), it's 1/2; for (b) sin² θ, it's 3/4; and for (c) sin(-θ), it's -√3/2.

Step-by-step explanation:

The student's original question: 'If 0=300 degrees, find the exact value of each expression below: (a) sin 0/2 (b) sin² 0 (c) sin (-0)' seems to have a typo because '0' is not an angle. We cannot find the sine of 'zero degrees' when the given angle is '300 degrees'. However, if we assume the student meant 'θ' (theta) to represent the angle, then the question would be correctly interpreted as finding the sine related values for 300 degrees:

1. (a) sin (θ/2) is sin (300°/2) or sin (150°). The exact value is 1/2 because 150° is in the second quadrant where sine is positive.
2. (b) sin² θ is sin² (300°). Since sin(300°) is - √3/2, squaring it gives 3/4.
3. (c) sin (-θ) is sin (-300°). Sine is an odd function, so sin (-θ) = -sin (θ). Hence, the value is √3/2.