Find all solutions
for cotx=-1​

whenever radians, where could be any integer (, which includes positive whole numbers, negative whole numbers, and zero.)

Step-by-step explanation:

(as in isoscele right triangles) would ensure that . Since cotangent is an odd function, .

Equivalently, when the angles are expressed in radians, .

The cycle of cotangent is (or equivalently, .) Therefore, if represents an integer, adding to the input to cotangent would not change the output. In other words:

.

Hence, would be a solution to whenever is an integer.

Since is the only solution to this equation in the period , all real solutions to this equation would be in the form (where is an integer.)

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: