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.

cot 30°

Accepted Answer

Welcome back, everyone determine the value of the trigonometric function tangent of 30 degrees or given for inter choices A squared of three divided by two B, one, a half C squared of two divided by two and D squared of three divided by three. So we can use a right triangle that contains an angle of 30 degrees. For this problem. Let's draw a right triangle. Let's draw an angle of 30 degrees and then the other angle is going to correspond to 60 degrees. Now let's suppose that the valley of the hypotenuse is equal to one that's the side land and now the opposite side in front of a 30 degree angle is equal to half of the hypotenuse. So we need to know at least this specific statement if our hypotenuse is equal to one, then the opposite side must be equal to one half of that, which is one half. And now let's suppose that the adjacent side is a, we can solve for a using the Pythagoras theorem which essentially states that the square of the hypotenuse is equal to the square of the opposite, which is one half squared plus the square of the adjacent, which is a squared, if we simplify, this means that one half is equal to 1/4 plus A squared. Now, if we subtract 1/4 from both sides, this leaves us with a squared equals 3/4. And if we take squared of both sides, A is equal to squared of three divided by two positive or negative, right? But since it is a side land, we are essentially taking a positive solution. And this means that A is squared of three divided by two. So we have our triangle and we have all of the required sidelines from here, we simply want to recall the definition of a tangent tangent is simply the ratio between the opposite side and the adjacent side, right. So if we take tangent of 30 degrees, we noticed that the opposite side, right, basically in front of that angle is equal to one half and the adjacent side is square of three divided by two. So we take the opposite side one half and we have to divide that by the length of the adjacent side squared of three divided by two. Since we have a ratio of two fractions, we can just rewrite the top fraction and multiply it by the reciprocal of the bottom one. So we are replacing that division with multiplication by the reciprocal, we can now cancel out the two and we end up with one divided by squares of three. And we want to rationalize it by multiplying both sides by the radical term in the denominator, which is squared of three, this gives us squared of three at the top and then scored of three multiplied by squared of three, gives us three in the denominator. And as we can see, the correct answer to this problem is option D squared of three divided by three. Thanks 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.
cot 30°

Key Concepts

Trigonometric Functions

Cotangent Function

Special Angles in Trigonometry

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