It's number 23
http://imageshack.us/f/855/screenshot201…
http://imageshack.us/f/855/screenshot201…
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I looked at #23. It appears there's a typo. The question asks you to find "q", but in all the answers they use "k". I think they meant "k" rather than "q" in the question.
Anyway, #1 is the best answer, although #4 is also correct. #2 and #3 are incorrect. Here's why:
sin kπ = 0 for any integer k. This includes sin 0, sin π, sin 2π, sin 3π, and so on (and sin -π too). Answer 1 fits this model.
Answer 4 is the same, but only for even multiples of π. So #4 is correct, but it's not as good as #1.
The other two answers, however, are incorrect. By adding π/2 (which is 90°), you're setting up 90° angles, and the sine of 90° (which is the sine of π/2) is one, not zero.
You wanted an explanation, so I hope this makes some sense to you.
Anyway, #1 is the best answer, although #4 is also correct. #2 and #3 are incorrect. Here's why:
sin kπ = 0 for any integer k. This includes sin 0, sin π, sin 2π, sin 3π, and so on (and sin -π too). Answer 1 fits this model.
Answer 4 is the same, but only for even multiples of π. So #4 is correct, but it's not as good as #1.
The other two answers, however, are incorrect. By adding π/2 (which is 90°), you're setting up 90° angles, and the sine of 90° (which is the sine of π/2) is one, not zero.
You wanted an explanation, so I hope this makes some sense to you.
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answer 1/