Inverse Trigonometry Calculator — arcsin, arccos, arctan
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Understanding Inverse Trigonometric Functions
Inverse trigonometric functions reverse the standard trig functions. Given a ratio, they return the angle. arcsin(0.5) = 30 degrees because sin(30) = 0.5. These functions are essential for finding angles from known side ratios.
Domain restrictions: arcsin and arccos only accept inputs from -1 to 1 (since sine and cosine only produce values in this range). arctan accepts all real numbers. The ranges are: arcsin returns [-90, 90], arccos returns [0, 180], arctan returns (-90, 90).
Inverse trig functions are used in navigation, robotics, computer graphics, and physics. They help determine angles of incidence, launch angles, and rotation angles from component measurements.
Frequently Asked Questions
What is the domain of arcsin?
arcsin accepts inputs from -1 to 1 only, because sine never produces values outside this range. Attempting to compute arcsin of 1.5, for example, is undefined.
Why does arccos(0.5) equal 60 degrees?
Because cos(60) = 0.5. The inverse cosine reverses this: given the cosine value 0.5, it returns the angle 60 degrees.
What is the difference between arctan and atan2?
arctan takes a single value and returns an angle in (-90,90). atan2(y,x) takes two arguments and returns the full angle in (-180,180), correctly handling all four quadrants.