Find the Determinant [[sin(theta),-1],[-1,sin(theta)]]

Problem

det(sin(θ))

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Substitute the values from the given matrix into the formula, where a=sin(θ) b=−1 c=−1 and d=sin(θ)

3. Multiply the diagonal elements and the off-diagonal elements.

sin(θ)⋅sin(θ)−(−1)⋅(−1)

4. Simplify the resulting expression using the notation sin2(θ) for the square of the sine function.

sin2(θ)−1

Final Answer

det(sin(θ))=sin2(θ)−1

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