Sketch the graph of $y=2\sin x + 1$ for intervals $0° \leq x \leq 360°$. Hence state the range of values of $x$ in this interval which satisfies the inequality $2\sin x + 1 \geq 0$.
The graph sketching part is easy but please can anyone explain how to find the range. Thanks
On
The graph sketching part is easy
If you have sketched the graph y=2sin x+1, then the question requires the values for which $y\ge 0$ i.e.,the regions of graph above x-axis.
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If you solve the equation $$2\sin x+1=0$$ in the specified range, you get $x=210°,330°.$ You can check that $2\sin x+1$ becomes $1$ at both endpoints of the given interval; thus by continuity it follows that the quantity is negative only for $x$ strictly between $210°$ and $330°.$ This gives you what you want.
This is simply asking you the following: For what values of $x$ is $\sin x \geq -\dfrac{1}{2}$? Does that help?