Question 1162249
here's how i think it's going to work.
you have sin(x) = -7/12
that makes x = -35.68533471.
add 360 to that to get the equivalent positive angle of 324.3146653.
the reference angle for that is 360 - that = 35.68533471.
the equivalent angle for that in the third quadrant is that plus 180 = 215.6853347.
take the sine of that and you get -7/12, which is the correct sine for angle x in the third quadrant.
you should be able to simply find sin(2x), cos(2x), tan(2x), by simply doubling that angle.
2 times 215.6853347 = 431.3706694.
you have:
x = 215.6853347
2x = 431.3706694
sin(2x) = .9476050057
cos(2x) = .3194444444.....
tan(2x) = 2.9664567.


if my assumptions are correct, those are your solutions.


using trigonometric identities, you shouls get the same answers.


you are given that sin(x) = -7/12
that makes x = 215.6853347, as we found out earlier.


the trigonometric identifies are:


sin(2x) = 2 * sin(x) * cos(x)
cos(2x) = cos^2(x) - sin^2(x)
tan(2x) = 2 * tan(x) / (1 - tan^2(x)


since we know x, we should be able to find those using the trig identities.


sin(x) = -.5833333333 stored in variable N
cos(x) = -,8133248621 stored in variable O
tan(x) = .7181848465 stored in variable P


i stored the values in those variables so i don't have to rewrite those values each time i use them.


the trigonometric identifies are rewritten using those variable names as shown below:


sin(2x) = 2 * N * O = .9476050057
cos(2x) = O^2 - N^2 = .3194444444
tan(2x) = 2 * P / (1 - P^2) = 2.96641567.


i get the same answers, so both methods seem to work.