1) if sin alpha = -4/5, and cos alpha> 0, find tan alpha and sec alpha. 2) if cot x = -3/2 and sec x< 0, find sin x and cos x. 3) if cos theta = 0.54, find sin(theta-pi/2). 4) if cot x = -0.18, find tan(x-pi/2). explain/show steps, i'm very lost on how to do these!

1)

cos(α) > 0, is just another way to say cos(α) is positive, and therefore, the adjacent side is positive then.

now, on -4/5, keep in mind that the hypotenuse is just a radius unit, and therefore is never negative, so in -4/5, the negative has to be the -4.





2)





hmm the sec(x) < 0, is just another way to say sec(x) is negative, and since the cosine is the reciprocal of the secant, then the cosine is also negative.  Now in the fraction -3/2, which is the negative?  since it could be -3/2 or 3/-2, well, anyhow, is the -3, because is the adjacent side, which is used by the cosine, that we know is negative.

We need more info then that