A point P(x, y) is shown on the unit circle corresponding to a...

Question

A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

Accepted Answer

Welcome back everyone. A point P 12 37th and negative 35 37th is plotted on the unit circle for a certain angle. Theta determine the values of the trigonometric functions. Sine theta cosine theta tangent, theta co tangent theta S theta and cos theta corresponding to this point. Here we have our unit circle with our angle. And for our answer choices A says the sign of theater is negative 35 37th. The cosine of theater is 12 37th. The tangent of theater is negative 35 12th. The core tangent of theater is negative 1235 35th. The C can of theta is 37 12th and the core C can of theta is negative 37 35th B says they are negative 35 37th, 1237 negative 12 35th, negative 35 1237 twelves and negative 37 35th C says they are 12 37th, negative 35 37th, negative 35 twelves, negative 35 35th, 3712 and negative 37 35th and D says they are 35 37th, negative 12 37th negative 35 twelves, negative 12, 35th, negative 37 twelves and 37 35th. Now let's look at our unit circle for some help. What do we know about our unit circle that's related to the values of trigonometric functions? Well, recall OK, that on the unit circle each, let me write that here. I don't know why I was writing writing unity circle, but I'm talking about the unit circle. OK? And on the unit circle, the XY coordinates are equal to the design to sorry to cost theta. OK. Cost theta and sign theater. In other words, the X coordinate is the cosine of theta and the Y coordinate is the sin of theta. Now that can prove pretty helpful. Let me just make some space here. That can prove pretty helpful because if we can use our unit circuit to figure out the values of cost theta and sign the, then we can figure out the rest of trigonometric functions. So let's go to our 0.12 37th and negative 35 37th. And now based on what we know that means the sine of theta is going to be the Y value negative 35 37th. Well, the cosine of theta is going to be the X value which is 12 37th. Now how can we use that to first help us figure out the tangent of the? Well, notice on our unit circuit, the tangent of the isn't explicitly written. But we know that the tangent is the ratio of the sine function to the core sine function. So we can divide sine theta by cost the to get the tangent of the. So that's going to be negative 35 37th. OK. Divided by 12, 37th or multiplied by its reciprocal 37 12th, 37 cancers 37. And that leaves us with negative 35 12th for the tangent of theta. Next, what is the core tangent going to be? Well, remember that the core tangent is simply the reciprocal of the tangent. So since the tangent is negative 35 12th, that must mean the core tangent is negative 12 35th. On the other hand, the sea can of theater, the second is the reciprocal of the cosine function. So since the cosine of theater is 12 37th, that means the second is gonna be 37 12th. Finally, we know that the Kosi can of theta is the reciprocal of the sin of theta. And since the sign of theta is negative 35 37th, that means the Kosi can must be negative 37 35th. Therefore, the sine of theta is negative 35 37th, the core sine is 12 37th, the tangent is negative 12, negative 3512. Sorry, the tangent is negative 35 12th. While the core tangent is negative 12, 35th, the C count is 37 12th and the core C count is negative 37 35th. If we look at our answer choices that tells us, then that a is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.
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Key Concepts

Unit Circle Definition

Trigonometric Functions on the Unit Circle

Evaluating Trigonometric Functions at a Given Angle

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