Questions: Looking at the graphs of y₁=sin x and y₂=-cos x+2, can you determine the solution set of sin x=-cos x+2 ? If so, what is it? If not, why not?

Transcript text: Looking at the graphs of $y_{1}=\sin x$ and $y_{2}=-\cos x+2$, can you determine the solution set of $\sin x=-\cos x+2$ ? If so, what is it? If not, why not?

Solution

Solution Steps

Step 1: Identify the graphs of y₁= sin(x) and y₂= -cos(x) + 2

The graph that oscillates around the x-axis is y₁= sin(x). The graph shifted upwards and oscillating around y=2 is y₂= -cos(x) + 2.

Step 2: Locate the intersection points

The two graphs intersect at one point. This point represents the solution to the equation sin(x) = -cos(x) + 2.

Step 3: Determine the solution set

The x-coordinate of the intersection point is π/2. Therefore, the solution set is {π/2}.

Final Answer

The solution set of sin(x) = -cos(x) + 2 is {π/2}.

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