Principal value in trigonometry refers to the unique angle within a specific range for which a trigonometric function takes a given value. For inverse trigonometric functions, the principal value is the angle that lies within a defined interval, ensuring a single and consistent output for each input.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions focuses on the inverse of trigonometric functions like sine and cosine and tangent or cosecant and secant and cotangent. It teaches how to find angles when the value of a trigonometric function is given. The chapter covers domains ranges graphs and solving equations of inverse trigonometric functions.
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To determine the principal value branch of cosec⁻¹x, let’s analyze the properties:
Step 1: Definition of the principal value branch
The principal value branch of cosec⁻¹x is defined such that:
1. It includes all possible values of the inverse cosecant function.
2. It avoids discontinuities or undefined values (like when cosec x = 0).
Step 2: Range of cosec⁻¹x
For cosec⁻¹x, the principal value is taken from the range:
[-π/2, π/2] – {0}
This excludes 0 because cosec x is undefined at sin x = 0.
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