SOLUTION: cos theta = 5/12 and tan theta is negative, find the exact valcue for sin theta.

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):
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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

Answer by chibisan(131)   (Show Source):
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=

Answer by jsmallt9(2063)   (Show Source):
You can put this solution on YOUR website!
cos(x) = adj/hyp
sin(x) = opp/hyp
tan(x) = opp/adj

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: