Homework Help: trig

Posted by Jared Smith on Monday, November 14, 2011 at 8:33pm.

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!

trig - Reiny, Monday, November 14, 2011 at 9:15pm
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

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