Match each trigonometric function in Column I with its value i...

Question

Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

sin 30°

Accepted Answer

Welcome back, everyone determine the value of the trigonometric function. We want to evaluate cosine of 30 degrees, an essential word given for an answer choices, a sub square root of three divided by two B, one half C squared of two divided by two and D squared of three divided by three. For this specific problem, we can just draw a right triangle. We want to make sure that it contains an angle of 30 degrees. So I suppose we have 30 degrees at the very top, we have a right triangle. So one of the angles is 90 degrees and this leaves us with an angle of 60 degrees. Let's suppose that our hypotenuse is equal to one. And we can essentially recall that the opposite side in front of or basically opposite to 30 degrees is equal to half of the hypotenuse. So we will have one half for the sideline of the opposite side. For the adjacent side, we can just use the Pythagorean theorem which says that the square of the hypotenuse must be equal to the square of the opposite. So one have squared less the adjacent side squared. Let's call it a. Now this gives us one equals 1/4 plus A squared. So that A squared is equal to three fours. And this means that A is equal to square root of three divided by two. Since we're taking square root of three words in this side, land must be positive. So we're only taking the positive solution. So now what we can do is just replace A with square of three divided by two. We're looking for cosine. And if we recall, according to so Katoa cosine is the ratio between the adjacent and the hypotenuse. So if we look at our angle of 30 degrees, this means that cosine of 30 degrees assembly, the ratio between the adjacent side, which is score of three divided by two. And now in our ratio, we have to include the length of the hypotenuse in the denominator, this is equal to one. So we end up with a square of three divided by two. This means that the correct answer to to this problem is a squared of three divided by two. Thank you for watching.

Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.
sin 30°

Key Concepts

Trigonometric Functions

Unit Circle

Special Angles

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