-0.5736
First we must find what sign tan-theta will have.
Sin-theta is negative, which means that theta must be in the 3rd or 4th quadrant of a graph. (from π radians (180˚) to 2π radians(360˚))
Now because cos-theta is greater than 0, it is positive, and cos-theta is only positive for values of theta in the 4th or 1st quadrant. The only possible choice is the 4th quadrant.
Tan-theta equals sin-theta/cos-theta. Because sin is negative and cos is positive, tan-theta will be a negative value.
Now to find the numerical answer.
Sin-theta in a triangle is equal to the opposite/hypotenuse. In this problem,
-0.5736 is the opposite. And the hypotenuse for all values of theta would be 1.
Create a right triangle where the leg opposite to value theta has a value of 0.5736, and where the hypotenuse is 1.
With a right triangle set up you can now use the Pythagorean theorem
a2+b2=c2
Where a and b are values for the legs and c is the value for the hypotenuse.
Using b for the leg opposite value theta, you manipulate the equation to work with the values found and you get:
c2-b2=a2
Plug in the values for c and b now.
12-(-0.5736)2=a2
1-0.3290=a2
0.671=a2
square root both sides
√0.671=a
0.819=a
(all values are rounded off the the thousandths place)
Now that you have the values for leg a and b, you can find the value for tan-theta.
Tan-theta equals opposite/adjacent or b/a in this case.
-0.5736/0.819=tan-theta
-0.700≈tan-theta
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There are 2 cups in a pint. There are 2 pints in a quart. There are 4 pints in a half gallon, like if you bought a half a gallon if milk at a store. There are 8 pints in a gallon. 10 pints equals 20 cups. 10 pints equals 5 quarts 10 pints equals 2 and a half gallons. 10 pints equals 1 and a quarter gallons. Hope I helped!
cotA*cotB*cotC = 1/[tanA+tanB+tanC]
f(x) = 1/x except where x = 0.
tan theta = sqrt(2)/2 = 1/sqrt(2).
copy this and paste in your browsers address window http://www.wolframalpha.com/input/?i=tan+theta+%2B+sec+theta+%3D1
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