A function in mathematics is a relation between a set of inputs and a set of possible outputs. Each input is related to exactly one output. Functions are often represented by equations or graphs and they are used to model real-world situations in various fields like physics, economics and engineering.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions focuses on the inverse of trigonometric functions such as sine and cosine and tangent or cosecant and secant and cotangent. It helps determine angles from given function values. The chapter covers domains ranges graphs and solving equations involving inverse trigonometric functions.
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We are asked to find sin[π/3 – sin⁻¹(-1/2)].
Step 1: Simplify sin⁻¹(-1/2)
The value sin⁻¹(-1/2) is the angle whose sine is -1/2, and the range of sin⁻¹ is [-π/2, π/2].
The angle that satisfies this condition is:
sin⁻¹(-1/2) = -π/6
Step 2: Substitute into the given expression
Now substitute sin⁻¹(-1/2) = -π/6 into the expression:
sin[π/3 – (-π/6)] = sin[π/3 + π/6]
Step 3: Simplify π/3 + π/6
Find a common denominator:
π/3 + π/6 = 2π/6 + π/6 = 3π/6 = π/2
Step 4: Calculate sin(π/2)
From the unit circle, sin(π/2) = 1.
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