In Exercises 1–4, a point P(x, y) is shown on the unit circle ...

Question

In Exercises 1–4, 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. In this problem, we want to determine the trigonometric function values for the real number represented by the point P and the unit circle where the point P is negative 24 25th and seven 25th. And the angle T is between the X axis and the line that forms O P from the origin to the point P. Now, what do we want to know? We want to know the trigonometric function values. OK. And we call that the trigonometric function values are that of the sign of the angle, the core sign of the younger and the tangent of the ankle. Also that means we need to find the cos of the angle we call second, the second of the angle and the tangent of the angle. No, we already know that these three, the C, the C and the core tangent are the reciprocal of the sign the cosine and the tangent respectively. So if we find the sign the cosine and the tangent, then we can re reciprocate them to get those other three, we also know that for the unit circle recall that on the unit circle, OK? On our unit circle or a pint is the cosine of the angle and the sign of the angle. In other words, the X value is the cosine and the Y value is the sign of the angle. So if we can use that to figure out the cosine and the sign, then we'll see where we go from there. So just by this property alone that tells us that the co sign is going to be negative 24 25th. Let me write that here and the sign of the angle is going to be seven 25th. So all we need to know is the tangent. What do we know about the tangent? Well, also recall that the tangent of an anger is equal to the sign of the anger divided by the cosine of the angle. So since we know the sign of the core sign, we can go ahead and solve for the tangent because the sign of the angle is seven 25th. So that's gonna be seven 25th divided by the core sign, which is negative 24 25th. Now let me rewrite that. So that's seven 25th multiplied by negative 25 divided by 24. Let me go ahead and simplify I can factor oh 25 from negative 25. So 25 sorry, negative 25 divided by 20 negative divided by 25 is negative one and 25 divided by 25 is one and then seven multiplied by negative one is negative seven and one multiplied by 24 is 24. So the tangent of T is equal to negative seven 24th know that I have the sign, the co sign and the tangent now that I have the sign, the cosine on the tangent, I'll be able to find a co which is the reciprocal of sign. So that's going to be, let me put that in purple 25 sevens. The second count is the in the reciprocal of the cosine of T. So that's negative 25 24th and the core tangent is the reciprocal of the tangent. So that is negative 24 7th and those would be our trigonometric val values at the point P. Thanks a lot for listening. I hope this video helped.

In Exercises 1–4, 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.

Key Concepts

Unit Circle Definition

Trigonometric Functions on the Unit Circle

Evaluating Trigonometric Functions for a Given Angle

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