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

Question

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

cos 28° < sin 28°

(Hint: sin 28° = cos 62°)

Accepted Answer

Hello. Today we're going to be determining whether the given statement is true or false. So we're asked to determine whether cosine of 47 degrees is less than sine of 47 degrees. So how can we approach this type of problem? Well, we have a co function formula that states that sine of theta is equal to cosine of 90 degrees minus the what this co function formula allows us to do is it allows us to rewrite sign in terms of cosine. And if we do that, we can rewrite the given statement in terms of cosine. So the angle that is given to us in the sine function is degrees. So if we plug in this value of data into the co function formula, we can state that sine of 47 degrees is equal to cosine of 90 minus 90 minus 47 will give us the value of 43. So sine of 47 degrees is equivalent to cosine of 43 degrees. And with that being said, we can rewrite the given statement as cosine of degrees is less than cosine of 43 degrees. Now, in order to answer this question, we're going to need to take a look at the graph of cosine. Let's go ahead and take a look at the graph of cosine. But we're going to restrict the graph to 90 degrees at the zero degree mark. The graph of cosine starts at positive one on the Y axis and at 90 degrees, the cosine function will be at negative one on the Y axis. And the shape of the function looks like half of a bell or half of an upside bell. So let's just say that 47 degrees or 43 degrees is roughly located about here. And we'll say that 47 degrees is located about here. As the graph of cosine is approaching 90 degrees, the graph is going to decrease in value over time. What this means is that the value of cosine of 43 degrees is going to be greater than cosine of 47 degrees. And with that being said, that means that the statement that is given to us is false and the overall answer 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. cos 28° < sin 28° (Hint: sin 28° = cos 62°)

Key Concepts

Trigonometric Ratios

Complementary Angles

Inequalities in Trigonometry

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