Question 1087132
i don't believe this is correct.


R * cos(T - a) = R * cos(T + a) becomes cos(T - a) = sin(T + a) when you divide both sides of the equation by R.


an example would be:


assume T = 50 and a = 10


the equation says that R * cos(40) = R * sin(60).


cos(40) = .7660444431


sin(60) = .8660254038


they're not the same.


it doesn't work because the angles are not complementary.


60 + 40 = 100, not 90.


the sum of the angles must be equal to 90 if the angles are complementary.


however, .....


cos(T - a) = sin(90 - T + a) will work because the angles are complementary.


if the angles are complementary, then (T - a) + (90 - T + a) must be equal to 90 degrees.


add them together and you get T - a + 90 - T + a is equal to 90.


so, unless i'm missing something .....,


R * cos(T - a) is not equal to R * sin(T + a).


however, .....


R * cos(T - a) is equal to R * sin(90 - T + a)


put it into degrees and use your calculator to find sine and cosine and you'll see what i mean.


note that sin(90 - T + a) is equal to sin(90 - (T - a))


you get cos(T - a) = sin(90 - (T - a)


the angles are complementary, and have to be in order for the equation to be correct.


cos(T-a) = sin(T+a) doesn't work.


cos(T-a) = sin(90-T+a) does work.


that's what i think.