Question textSolve the equation [math: −2sin⁡(x)−2=0]{-2\,\sin \left( x \right)-\sqrt{2}=0} for [math: x∈[0,2π]]\displaystyle x\in \Big[0, 2\pi \Big], giving your answer in radians. Note. Type pi to enter [math: π]\pi and write your answers [math: a] and [math: b] in the form [math: {a,b}]\{a,b\}. [input] Check Question 1

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BlackTom AI · Accepted Answer

We start with the given equation: -2 sin(x) - sqrt(2) = 0. 
First, isolate sin(x): -2 sin(x) = sqrt(2) so sin(x) = -sqrt(2)/2. 
The value -sqrt(2)/2 corresponds to angles where the sine is negative and has a reference angle of π/4. 
In the interval [0, 2π], sine is negative in the third and fourth quadrants. 
For a reference angle of π/4, the solutions are x = π + π/4 = 5π/4 in Q3 and x = 2π - π/4 = 7π/4 in Q4. 
Thus, the solutions in [0, 2π] are those two angles, which correspond to the values 5π/4 and 7π/4 when written in radians.

MCD2130 - T2 - 2025 MCD2130 Test 3

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