Question 33858: cos theta = 5/12 and tan theta is negative, find the exact valcue for sin theta. Found 3 solutions by venugopalramana, chibisan, jsmallt9:Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website! cos theta = 5/12 and tan theta is negative, find the exact valcue for sin theta.
USING ALL SILVER TEA CUPS,SINCE COS IS +VE AND TAN IS -VE,THETA IS IN IV Q.WHERE SINE IS ALSO -VE.
HENCE COMPLETING TRIANGLE
12^2=5^2+X^2
X=SQRT(144-25)=SQRT(119)
HENCE SIN(THETA)= -SQRT(119)/12
You can put this solution on YOUR website! cosθ = 5/12 and tanθ is negative , find the exact value for sinθ
since cosine is positive , it lies on the 1st quadrant
cosθ = adj/hyp = 5/12
sinθ = opp/hyp
by pythagoras theorem find the opp.
sinθ=
We are given that cos(x) = 5/12 so we can use 5 for the adjacent side and 12 for the hypotenuse. By the Pythagorean Theorem, so:
Simplifying we get:
Subtracting 25 from each side we get:
Finding the square root of each side we get:
Since tan(x) is negative and tan(x) is opp/hyp and the hypotenuse is always positive, the opposite side must be negative. So:
and so, since sin(x) = opp/hyp:
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