QuestionIdentify which equation does not define a trigonometric function for a point $P(x, y)$ on the unit circle: A. $\cot t=\frac{y}{x}, x \neq 0$ B. $\csc t=\frac{1}{y}, y \neq 0$ C. $\cos t=x$ D. $\sec t=\frac{1}{x}, x \neq 0$

Studdy Solution

STEP 1

Assumptions1. $(x, y)$ is a point on the unit circle corresponding to $t$ . $t$ is a real number3. The trigonometric functions are defined as follows - $\cot t = \frac{y}{x}$ , $x \neq0$ - $\csc t = \frac{1}{y}$ , $y \neq0$ - $\cos t = x$ - $\sec t = \frac{1}{x}$ , $x \neq0$

STEP 2

We need to determine which of the given equations does not accurately define a trigonometric function. Let's start with option A.
Option A $\cot t = \frac{y}{x}$ , $x \neq0$
This is the correct definition of the cotangent function in terms of $x$ and $y$ coordinates on the unit circle, where $x$ is not equal to zero.

STEP 3

Next, let's consider option B.
Option B $\csc t = \frac{1}{y}$ , $y \neq0$
This is the correct definition of the cosecant function in terms of $x$ and $y$ coordinates on the unit circle, where $y$ is not equal to zero.

STEP 4

Now, let's consider option C.
Option C $\cos t = x$
This is the correct definition of the cosine function in terms of $x$ and $y$ coordinates on the unit circle.

STEP 5

Finally, let's consider option D.
Option D $\sec t = \frac{1}{x}$ , $x \neq0$
This is not the correct definition of the secant function. The secant function is defined as the reciprocal of the cosine function, and in terms of $x$ and $y$ coordinates on the unit circle, it should be $\sec t = \frac{1}{\cos t} = \frac{1}{x}$ , where $x$ is not equal to zero.
Therefore, the equation that does not accurately define a trigonometric function is option D $\sec t = \frac{1}{x}$ , $x \neq0$ .

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