Evaluate cot -220o
Round your answer to the nearest hundredth.
A. -1.31
B. 1.56
C. -1.19
D. -0.84
-220 = 360 - 220 = 140
which is 180 - 40
which is 40 degrees above the -x axis in quadrant 2
tan and cot are negative in Q2
tan 40 = .839
so cot 40 = 1/.839 = 1.19
BUT it is negative so
-1.19 <------------
cot -220 = 1.19
what, your calculator doesn't do tan x in degrees?
cot x = 1/tan x
To evaluate cot -220o, we need to use the unit circle or trigonometric functions.
The cotangent function (cot) is defined as the reciprocal of the tangent function (tan). The tangent of an angle is given by the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
To evaluate cot -220o, we first need to find the reference angle. We can do this by adding 360o to -220o until we get a positive angle less than 360o.
-220o + 360o = 140o
The reference angle is 140o.
Next, we need to find the sine (sin) and cosine (cos) of the reference angle. We can do this by using the unit circle or a calculator.
sin 140o ≈ -0.985
cos 140o ≈ 0.174
Finally, we can evaluate the cotangent (cot) using the formula cot = cos / sin.
cot -220o ≈ cos 140o / sin 140o ≈ 0.174 / -0.985 ≈ -0.1766
Rounding to the nearest hundredth, we get -0.18.
Therefore, the answer is not one of the options given.