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Home›Function Tools›Inverse Trig Function Evaluator

Inverse Trig Function Evaluator

Evaluate arcsin, arccos, and arctan of a given value

Select Function
arcsin()

Inverse Trig Properties

arcsin(x): domain [-1,1], range [-pi/2, pi/2]
arccos(x): domain [-1,1], range [0, pi]
arctan(x): domain R, range (-pi/2, pi/2)
sin(arcsin(x))=x, arcsin(sin(x))=x (restricted)

Inverse trigonometric functions find the angle corresponding to a given trig ratio. They are defined on restricted domains to ensure unique values. The result can be expressed in radians or degrees.

⚠ arcsin(x)=y means sin(y)=x AND y is in [-pi/2, pi/2]. The restricted range ensures a unique output.

What Are Inverse Trig Functions?

Inverse trig functions answer: what angle has this sine/cosine/tangent? arcsin(0.5)=pi/6 because sin(pi/6)=0.5. They are essential in solving trigonometric equations, integration, and geometry calculations.

arcsin(x)

Inverse of sine. Range [-pi/2, pi/2]. arcsin(1)=pi/2, arcsin(0)=0, arcsin(-1)=-pi/2.

arccos(x)

Inverse of cosine. Range [0, pi]. arccos(1)=0, arccos(0)=pi/2, arccos(-1)=pi.

arctan(x)

Inverse of tangent. Range (-pi/2, pi/2). arctan(1)=pi/4. Horizontal asymptotes at +/- pi/2.

Relations

arcsin(x)+arccos(x)=pi/2. arctan(x)+arccot(x)=pi/2. These identities relate inverse trig functions.

Teaching Example: arcsin(0.5). We need an angle in [-pi/2, pi/2] with sin=0.5. Answer: pi/6=30. Check: sin(pi/6)=0.5. In degrees: arcsin(0.5)=30.

Applications

Trigonometry Calculus Physics Engineering Navigation

Frequently Asked Questions

What is arcsin(x)?▼
Angle whose sine is x. Range [-pi/2, pi/2]. arcsin(0.5)=pi/6. Only defined for |x|<=1.
arcsin vs arccos?▼
arcsin: [-pi/2, pi/2], arccos: [0, pi]. arcsin(x)+arccos(x)=pi/2 for x in [-1,1].
arctan domain?▼
Domain: all real numbers. Range: (-pi/2, pi/2). Horizontal asymptotes at y=pi/2 and y=-pi/2.
Convert radians to degrees?▼
Multiply by 180/pi. pi rad=180. pi/6=30, pi/4=45, pi/3=60, pi/2=90.

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