trig
posted by Jared Smith .
If sin(t) = 2/48 and cos(t) < 0 what is the value of cos(t) to the nearest thousandth?
If sin(t) = 14/34 and cos(t) < 0, what is the value of tan(t) to the nearest thousandth?
If tan(t) = 15/19 and sin(t) < 0, what is sin(t) to the nearest thousandth?
If tan(t) = 11/12 and sin(t) < 0, what is cos(t) to the nearest thousandth?
The path of a projectile fired at an inclination t0 to the horizontal with initial velocity v feet per second is a parabola. The horizontal distance R, in feet, that the projectile travels is given by R = v2sin(2t)/32.2. What is R if v = 152 and t = 74? Give your answer to the nearest thousandth.
Show the steps please!

I will do the first, then you do the remaining ones in the same way
sin t = 2/48 = 1/24 and cos t < 0
therefore t must be in quadrant III ( by CAST rule)
I make a triangle, the missing side is x
x^2 + 1^2 = 24^2
x = √575
then in III, cos t = √575/24 = appr. .999
or
take sin^1 (+1/24) to get 2.388°
so in III , t = 180+2.388 = 182.388°
cos 182.388° = appr. .999