Trigonometry
Class 12

Inverse Trigonometric Functions

sin1x+cos1x=π2\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}
−1−0.500.511.5707963267948966
sin⁻¹(x) + cos⁻¹(x) = π/2

Fundamental relationship between inverse sine and cosine. Other identities: tan⁻¹x + cot⁻¹x = π/2.

Real-World Applications

Navigation — Converting between bearing and angle formats.

Robotics — Inverse kinematics for robot arm positioning.

Computer graphics — Camera angle calculations.

Physics — Angle of refraction in optics.

Surveying — Calculating angles from distance measurements.

Astronomy — Converting celestial coordinates.

Architecture — Roof pitch calculations.

Engineering — Gear angle specifications.

Sports science — Launch angle optimization.

Medical imaging — Image reconstruction algorithms.

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