The inverse function of cotangent.
You are watching: Cot^-1(-1)
Basic idea: To find cot-1 1, we ask "what angle has cotangent equal to 1?" The answer is 45°. As a result we say cot-1 1 = 45°. In radians this is cot-1 1 = π/4.
More: Tbelow are actually many angles that have actually cotangent equal to 1. We are really asking "what is the simplest, the majority of standard angle that has cotangent equal to 1?" As before, the answer is 45°. Thus cot-1 1 = 45° or cot-1 1 = π/4.
Details: What is cot-1 (–1)? Do we select 135°, –45°, 315°, or some other angle? The answer is 135°. With inverse cotangent, we select the angle on the optimal fifty percent of the unit circle. Thus cot-1 (–1) = 135° or cot-1 (–1) = 3π/4.
In various other words, the variety of cot-1 is identified to be the angles on the upper fifty percent of the unit circle as pictured below. The selection of cot-1 is limited to (0, 180°) or (0, π).
Note: arccot refers to "arc cotangent", or the radian measure of the arc on a circle equivalent to a offered worth of cotangent.
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Technical note: Due to the fact that none of the six trig attributes sine, cosine, tangent, cosecant, secant, and also cotangent are one-to-one, their inverses are not functions. Each trig function can have actually its domain minimal, but, in order to make its inverse a role. Some mathematicians create these minimal trig features and their inverses via an initial capital letter (e.g. Cot or Cot-1). However, most mathematicians carry out not follow this exercise. This website does not differentiate between capitalized and also uncapitalized trig attributes.
Inverse trigonometry, inverse trig features, interval notation