In Exercises 55–58, use a graph to solve each equation for -2π ≤ ...

Question

In Exercises 55–58, use a graph to solve each equation for -2π ≤ x ≤ 2π.

csc x = 1

Accepted Answer

Welcome back. I am so glad you're here. We're asked to solve the given equation with the help of the graph of negative two pi is less than or equal to X is less than or equal to two pi. And our given equation is the Cosic can of X equals two. And then we have a graph. Our graph has a vertical Y axis. A horizontal X axis. They come together at the origin in the middle. The domain of our graph is from negative two pi to two pi. And the range of our graph is from negative 3 to 3. And on the graph is the coy can of X. Our answer choices are answer choice A na the solution set for negative three pi divided by two and pi divided by two answer choice B the solution set negative 11 pi divided by six, negative seven pi divided by six pi divided by six and five pi divided by six answer choice C the solution set negative pi divided by two and three pi divided by two and answer choice D the solution set negative five pi divided by six negative pi divided by 67 pi divided by six and 11 pi divided by six. All right. This one's really neat because as we look at our graph, we have the coy can of X on there. And what we're trying to solve for is the X value when our Y value is two, we know that the co can of X is equal to Y. And so because the co C can of X is equal to two here, our Y values are two, we just need to find the corresponding X values when Y equals two. So from the origin, if we go up two units and we look along that where Y is equal to two, look along that unwritten line where our coy can of X intersects with two, we have X values of negative pi divided by six, negative seven pi divided by six pi divided by six and five pi divided by six. And that solution set is our answer. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

In Exercises 55–58, use a graph to solve each equation for -2π ≤ x ≤ 2π. csc x = 1

Key Concepts

Cosecant Function

Graphing Trigonometric Functions

Periodic Nature of Trigonometric Functions

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