Question 946102: If tanq=-0.09 and q is in Quadriant 4, find the value of cosq.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tan(q) = -.09
q is in quadrant 4.
find the value of cos(q).
if q was in quadrant 1, it's tangent would be .09
using your calculator, the angle in quadrant 1 whose tangent is .09 is equal to 5.142764558 degrees.
5.142764558 degrees is the reference angle.
the equivalent angle in quadrant 4 is equal to 360 - 5.142764558 which is equal to 354.8572354 degrees.
using your calculator, the cosine of 354.8572354 degrees is equal to .9959744388.
you can confirm using your calculator.
tan(354.8572354) = -.09
cos(354.8572354) = .9959744388
there is another way to find it without resorting to using the calculator.
this involves knowledge of the unit circle.
in the unit circle, the hypotenuse of a triangle is always equal to 1.
you know that tan(q) is equal to -.09
the tangent function in the unit circle is equal to y/x.
you get y/x = -.09
solve for y to get y = -.09x.
your x value in the unit circle is equal to x.
your y value in the unit circle is equal to -.09x.
your hypotenuse in the unit circle is always equal to 1.
by pythagorus, x^2 + y^2 = h^2 where h is the hypotenuse of the right triangle formed by x and y.
this equation becomes x^2 + (-.09x)^2 = 1^2
simplify to get x^2 + .0081x^2 = 1
combine like terms to get 1.0081x^2 = 1
divide both sides of this equation by 1.0081 to get x^2 = 1/.0081 = .9919650828.
take the square root of both sides of this equation to get x = .9959744388.
solve for y to get y = -.09x = -.09 * .9959744388 = -.0896376995
you now have:
hypotenuse = 1
x = .9959744388
y = -.0896376995
tan(q) = y/x = -.0896376995 / .9959744388 = -,09
cos(q) = x / h = x / 1 = x = .9959744388.
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