Determine whether each statement is true or false. If false, tell...

Question

Determine whether each statement is true or false. If false, tell why.

csc 22° ≤ csc 68°

Accepted Answer

Identify if the given statement is true or false, provide the justification. If it is false, we have co sequent 34 degrees is less than it equals to cos of 56 degrees. We wanna see if this is true or false. Now, we can start by looking at the property of, of coke. We now cos data as equals to one divided by a sign what we know. So is Y divided by R in our case, then sequent will be the reciprocal which is R divided by Y. Now we know this, let's see what happens if we hold R to be fixed. So they are some fixed value. Usually it's one but we don't know that for sure. And we'll see what happens to our function. So if we hold our fixed, we'd be increasing our angle. If we increase our angle, our Y also increases. Other words, data increase gives us a wide increase. Now, since our fraction on the denominator is getting larger with every the increase, our co sequent data overall is getting smaller. If we hold our fix, the Y is getting larger, which means we get a smaller fraction every time in other words, gets smaller with larger of values. Now, if we know this, we can look at our function, we have 56 degrees should be greater than 34 degrees, which is true. However, our statement says co sequent 34 is less than or equal to co sequent based on what we just determined, that is not true. CO N 34 should be larger than coin 56 because of our smaller angle. This means our answer is answer B this is false for a fixed value of R as data increases, cos and data decreases. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

Determine whether each statement is true or false. If false, tell why. csc 22° ≤ csc 68°

Key Concepts

Cosecant Function

Angle Relationships in Trigonometry

Inequalities in Trigonometric Functions

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