Simplifying Trigonometric Expressions With Radian Angles: Solving Sin 3๐œ‹/2 ๐‘œ๐‘Ÿ (9๐œ‹/6) ๐‘œ๐‘Ÿ (6๐œ‹/4) = 1.

sin 3๐œ‹/2 ๐‘œ๐‘Ÿ (9๐œ‹/6) ๐‘œ๐‘Ÿ (6๐œ‹/4)

-1

First, we need to convert the angles to radians:

– 3๐œ‹/2 is already in radians
– 9๐œ‹/6 simplifies to 3๐œ‹/2, which we already know is equal to -๐œ‹/2.
– 6๐œ‹/4 simplifies to 3๐œ‹/2, which we also know is equal to -๐œ‹/2.

So, we can rewrite the expression as:

sin(-๐œ‹/2) * sin(-๐œ‹/2)

Now, we can use the identity sin(-๐œƒ) = -sin(๐œƒ) to simplify further:

(-1) * (-1) * sin(๐œ‹/2) * sin(๐œ‹/2)

sin(๐œ‹/2) = 1, so we end up with:

1 * 1 = 1

Therefore, sin 3๐œ‹/2 ๐‘œ๐‘Ÿ (9๐œ‹/6) ๐‘œ๐‘Ÿ (6๐œ‹/4) = 1.

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