Question

Arcsin(-x) = arccos(-x)= artg(-x)= arcctg(-x)=

Answer 1

arcsin(-x) =-arcsinx

arccos(-x)=П-arccosx

arctg(-x)=-arctgx

arcctg(-x)=П-arcctgx

Answer 2

The equations you've provided relate different trigonometric functions to the same input value, -x. Here's how each of these equations breaks down:

1. arcsin(-x): This represents the inverse sine function, which gives you an angle whose sine is -x. In this context, it means you're looking for an angle in a right triangle where the opposite side is -x and the hypotenuse is 1. The solution is typically found in the interval [-π/2, π/2], and it's the angle θ such that sin(θ) = -x.

2. arccos(-x): This represents the inverse cosine function, which gives you an angle whose cosine is -x. Similar to arcsin, it means you're looking for an angle in a right triangle where the adjacent side is -x and the hypotenuse is 1. The solution is also typically found in the interval [0, π], and it's the angle θ such that cos(θ) = -x.

3. artg(-x): "artg" is not a commonly used abbreviation for a trigonometric function. It's possible that you mean "arctan," which represents the inverse tangent function. If that's the case, it gives you an angle whose tangent is -x. In a right triangle, this means you're looking for an angle θ such that tan(θ) = -x. The solution is typically found in the interval (-π/2, π/2).

4. arcctg(-x): "arcctg" is not a commonly used abbreviation for a trigonometric function either. It's possible that you mean "arccot" or "arccotangent," which represents the inverse cotangent function. This gives you an angle whose cotangent is -x. In a right triangle, it means you're looking for an angle θ such that cot(θ) = -x. The solution is typically found in the interval (0, π).

So, each of these equations represents an angle associated with a specific trigonometric ratio and the input value -x. The actual values of these angles would depend on the value of -x and the specific trigonometric function being used.