Find Theta in the degree measure for the indicated quadrant. Show the diagram.
cot (Theta)= -(Radical 3/1)in quadrant IV.
I got 240 degrees but i don't know how to do the diagram since 240 degrees is in quadrant III. How do you put this in a diagram?
sqrt 3 is greater than one, how can the Cosine be greater than one?
Do i have to change it from cot to cos?
oops. It is ctn. I read it as cosine. Duh.
OK, ctn Theta= -sqrt3
or TanTheta=-1/sqrt3
but drawing a small triangle, that means the hypotenuse is 2, and cosine= sqr3 / 2, sin theta= -1/2 Well, I recognize sin=-1/2 as - 30 deg, so the quadrant IV angle then is 330.
To find the angle Theta in the degree measure for the indicated quadrant, we can start by identifying the given information: cot(Theta) = -(√3/1) in quadrant IV.
To create a diagram, we'll start with the coordinate plane. In the coordinate plane, Quadrant IV is the bottom-right quadrant.
Since cotangent is the reciprocal of the tangent function, we can find the tangent of Theta by taking the reciprocal of -(√3/1). The reciprocal of -(√3/1) is -(1/√3).
Next, we can recall that the tangent is the ratio of the opposite side over the adjacent side in a right triangle. Since the horizontal side in Quadrant IV is the adjacent side and the vertical side is the opposite side, the ratio of these sides will be -(1/√3), which is equal to the tangent of Theta.
To solve for Theta, we can use the inverse tangent function (tan^(-1)). Taking tan^(-1) of -(1/√3) gives us the angle in the first quadrant.
However, since we want Theta to be in quadrant IV, we need to determine the equivalent angle in Quadrant IV. In the first quadrant, the angle obtained from tan^(-1)(-(1/√3)) is approximately 330. In Quadrant IV, the reference angle is obtained by subtracting the angle from 360 degrees.
Therefore, the equivalent angle in Quadrant IV for Theta is 360 - 330 = 30 degrees.
To summarize, the angle Theta in the degree measure for the indicated quadrant is 30 degrees.