Determine whether each statement is true or false. See Example 4....

Question

Determine whether each statement is true or false. See Example 4.

csc 20° < csc 30°

Accepted Answer

Hello. Today, we're going to be determining whether the given statement is true or false. So we are asked to determine whether co sequent of degrees is less than co sequent of 88 degrees. Now, in order to answer this question, we're going to need to take a look at the first period of the graph of the function. So let's just go ahead and draw the first period of the COKING function. Now, the first period of the coin function has two asymptotes. The first ascent tote is located at zero or zero degrees and the second Aceto is located at PI which is equivalent to 180 degrees. The Cos Seeking graph has a rough shape like this and this is where we are given a point at pi divided by two comma one or which can be rewritten as 90 degrees comma one. So we can roughly estimate that degrees is located about here. And let's go ahead and say that 88 degrees is roughly located here. Now, as the co seeking graph is approaching the 90 degree mark, the value of coin is decreasing over time. So what this means is that the value of 67 degrees on the co seeking graph is going to be greater than the value of coin of degrees. And with that being said, that means that this inequality is false. And the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Determine whether each statement is true or false. See Example 4. csc 20° < csc 30°

Key Concepts

Cosecant Function

Angle Comparison

Trigonometric Inequalities

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