Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles. It involves functions like sine, cosine and tangent, which are used to solve problems in geometry, physics, engineering and many other fields. It is fundamental to understanding wave patterns and oscillations.
Inverse Trigonometric Functions in Class 12 Maths focus on the inverse of basic trigonometric functions like sine, cosine, tangent, cosecant, secant and cotangent. These functions help find the angle when the value of a trigonometric function is given. The chapter covers domains, ranges and graphical representations, along with solving equations involving inverse trigonometric functions.
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We are given that y = cot⁻¹x and x < 0. We need to find the range of y.
Step 1: Recall the range of cot⁻¹x
The range of the inverse cotangent function cot⁻¹x is (0, π) for all real x.
Step 2: Analyze the condition x < 0
When x < 0, the value of y = cot⁻¹x lies in the interval (π/2, π), because the cotangent function is negative in this interval.
Final Answer:
Thus, the range of y is π/2 < y ≤ π.
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