CONCEPT PREVIEW Match each trigonometric function in Column I wit...

Question

CONCEPT PREVIEW 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.     I                           II1.                        A. √32.                        B. 13. tan 45°            C. ½4.                        D. √35.                              26.                        E. 2√3                                 3                           F. √3                                3                           G. 2                           H. √2                                2                            I. √2

Accepted Answer

Welcome back, everyone. In this problem, we want to find the exact value of the trigonometric function that of the tangent of 30 degrees. For our answer choices A is one B is the square root of three divided by three C is the square root of three and D is zero. Now, to help us figure out what the exact value of our function. The tangent of 30 degrees is. It's best we use our unit triangle for a 30 60 right triangle. So let me draw a sketch of that over here on the right. OK. And recall that for that triangle for that right triangle where we have one angle being 60 degrees and one angle being 30 degrees. Then the side adjacent to the 60 degree angle would be one, the hypotenuse would be of unit length two and the side adjacent to the 30 degree angle, the remaining side would be the square root of three. So that can help us to figure out the value of the tangent of 30. Because also recall that the tangent of an anger equals the opposite side. It's the ratio of the opposite side to the adjacent side. So if we take our angle and find our opposite and adjacent side respectively, then we will be able to figure out the exact value of the tangent of 30. So first, let's label our sides. So because we're talking about the 30 degree angle, OK, then the side opposite to it would have been the side with unit length one and the side adjacent to it would have been the side with unit length square root of three. Therefore, that means that the tangent of 30 degrees would be equal to the opposite side, which is one divided by the adjacent side, which is the square root of three. No, we're almost there. Our denominator is a radical. So we need to rationalize so that we can simplify. So to rationalize, we can multiply our expression by the square root of three in the numerator and the square root of three in the denominator one multiplied by the square of three equals the square of three and the squared of three multiplied by the square root of three equals three. So that means the tangent of 30 degrees equals the square root of three divided by three. And when we look in our answer choices, that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

CONCEPT PREVIEW 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. I II1. A. √32. B. 13. tan 45° C. ½4. D. √35. 26. E. 2√3 3 F. √3 3 G. 2 H. √2 2 I. √2

Key Concepts

Trigonometric Functions

Special Angles

Unit Circle

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