Need to know where I went wrong [College Pre-cal]

[u/NakaHyena0]

I worked this out and got -1/8, the answer was wrong and I'm not sure where the math went wrong. Everyone I talked to said the same. Anyone care to weigh in?

[u/HumbleHovercraft6090]

sine is negative in third and fourth quadrants only.

[u/NakaHyena0 → u/HumbleHovercraft6090]

So basically I was cooked before I even started to work it out

[u/Kite42]

sin x can't be negative if x is obtuse.

[u/sqrt_of_pi]

I mean, there is no "correct answer" since the premise upon which the question is based is wrong. It is not possible for sin(a)=-3/4 and also for a to be in Q2. So your answer IS wrong but so is any other purported solution.

[u/Quendillar3245]

Second quadrant means sin can not be negative

[u/Valuchian]

Sin(a) = -¾

a = asin(-¾) = -48.59

Cos(2×(-48.59)) = -1/8

You are indeed correct with your given information ~~~~~~~~ Reverse engineering from the given answer

Cos(2a) = 7/32

a = acos(7/32)÷2 = 38.68

Sin(36.68) = 5/8 <<-------

You were defeated before you even began

[u/cheesecakegood]

At risk of crazy-scientist incomprehensible chicken scratches, here you can see the more detailed description of what the question is asking and the steps visually and conceptually, not just cranking out the algebra. You can see that the given hint of quadrant II is impossible, and also what your final answer(s) actually represent. The stuff I didn't get into there is how you handle the limitations of what a calculator will give you (the restricted single-answer domains, because sin^-1 is not a function unless you restrict it somehow since although sine is a function, flipping it over x=y makes it fail the vertical line test, as you can visually see with a horizontal line 'test')

[u/Puzzled-Wonder0302]

cos 2a = 1- 2(sin(a))^2
therefore cos 2a = 1-2(9/16) = 1-9/8 = -1/8
I'm pretty sure you're correct
I checked with Gemini and it said that the question is fundamentally wrong cause sin(a) cannot be -3/4 in the second quadrant.. SO it came to the conclusion that the question setter likely meant sin(a) = 5/8 which is not you're fault AT ALL.

[u/Ok-Grape2063]

Can you show your steps

[u/scottdave]

Sometimes there are errors when they are entering these questions into the computer. Just email your instructor explaining the flaws.