Question Find the value of $y$ for each $x$ given the expression $y=-4 \cos (x)$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $y=-4 \cos (x)$ . We need to find the value of $y$ for a given value of $x$
3. We assume that $x$ is in radians

STEP 2

The cosine function, $\cos(x)$ , gives the ratio of the adjacent side to the hypotenuse in a right triangle. It varies between -1 and1 for all values of $x$ .

STEP 3

The expression $y=- \cos (x)$ is a transformation of the cosine function, where the amplitude (the peak value) of the function is multiplied by -.

STEP 4

To find the value of $y$ for a given value of $x$ , we simply substitute the value of $x$ into the expression and calculate the result.
$y=-4 \cos (x)$

STEP 5

For example, let's find the value of $y$ when $x =0$ .
$y=-4 \cos (0)$

STEP 6

We know that $\cos(0) =1$ , so we substitute this into the expression.
$y=-4 \times1$

STEP 7

Calculate the value of $y$ .
$y=-4$ So when $x =0$ , $y = -4$ .

STEP 8

Similarly, we can find the value of $y$ for any given value of $x$ by substituting the value of $x$ into the expression and calculating the result.
For example, to find the value of $y$ when $x = \pi/2$ , we substitute $\pi/2$ into the expression.
$y=-4 \cos (\pi/2)$

STEP 9

We know that $\cos(\pi/2) =$ , so we substitute this into the expression.
$y=-4 \times$

STEP 10

Calculate the value of $y$ .
$y=0$ So when $x = \pi/2$ , $y =0$ .

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Question Find the value of $y$ for each $x$ given the expression $y=-4 \cos (x)$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $y=-4 \cos (x)$ . We need to find the value of $y$ for a given value of $x$
3. We assume that $x$ is in radians

STEP 2

The cosine function, $\cos(x)$ , gives the ratio of the adjacent side to the hypotenuse in a right triangle. It varies between -1 and1 for all values of $x$ .

STEP 3

The expression $y=- \cos (x)$ is a transformation of the cosine function, where the amplitude (the peak value) of the function is multiplied by -.

STEP 4

To find the value of $y$ for a given value of $x$ , we simply substitute the value of $x$ into the expression and calculate the result.
$y=-4 \cos (x)$

STEP 5

For example, let's find the value of $y$ when $x =0$ .
$y=-4 \cos (0)$

STEP 6

We know that $\cos(0) =1$ , so we substitute this into the expression.
$y=-4 \times1$

STEP 7

Calculate the value of $y$ .
$y=-4$ So when $x =0$ , $y = -4$ .

STEP 8

Similarly, we can find the value of $y$ for any given value of $x$ by substituting the value of $x$ into the expression and calculating the result.
For example, to find the value of $y$ when $x = \pi/2$ , we substitute $\pi/2$ into the expression.
$y=-4 \cos (\pi/2)$

STEP 9

We know that $\cos(\pi/2) =$ , so we substitute this into the expression.
$y=-4 \times$

STEP 10

Calculate the value of $y$ .
$y=0$ So when $x = \pi/2$ , $y =0$ .

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Question Find the value of yyy for each xxx given the expression y=−4cos⁡(x)y=-4 \cos (x)y=−4cos(x).

Studdy Solution

STEP 1

Assumptions1. The given expression is y=−4cos⁡(x)y=-4 \cos (x)y=−4cos(x). We need to find the value of yyy for a given value of xxx3. We assume that xxx is in radians

STEP 2

The cosine function, cos⁡(x)\cos(x)cos(x), gives the ratio of the adjacent side to the hypotenuse in a right triangle. It varies between -1 and1 for all values of xxx.

STEP 3

The expression y=−cos⁡(x)y=- \cos (x)y=−cos(x) is a transformation of the cosine function, where the amplitude (the peak value) of the function is multiplied by -.

STEP 4

To find the value of yyy for a given value of xxx, we simply substitute the value of xxx into the expression and calculate the result.y=−4cos⁡(x)y=-4 \cos (x)y=−4cos(x)

STEP 5

For example, let's find the value of yyy when x=0x =0x=0.y=−4cos⁡(0)y=-4 \cos (0)y=−4cos(0)

STEP 6

We know that cos⁡(0)=1\cos(0) =1cos(0)=1, so we substitute this into the expression.y=−4×1y=-4 \times1y=−4×1

STEP 7

Calculate the value of yyy.y=−4y=-4y=−4So when x=0x =0x=0, y=−4y = -4y=−4.

STEP 8

STEP 9

We know that cos⁡(π/2)=\cos(\pi/2) =cos(π/2)=, so we substitute this into the expression.y=−4×y=-4 \timesy=−4×

STEP 10

Calculate the value of yyy.y=0y=0y=0So when x=π/2x = \pi/2x=π/2, y=0y =0y=0.

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Question Find the value of $y$ for each $x$ given the expression $y=-4 \cos (x)$ .

Assumptions1. The given expression is $y=-4 \cos (x)$ . We need to find the value of $y$ for a given value of $x$
3. We assume that $x$ is in radians

The cosine function, $\cos(x)$ , gives the ratio of the adjacent side to the hypotenuse in a right triangle. It varies between -1 and1 for all values of $x$ .

The expression $y=- \cos (x)$ is a transformation of the cosine function, where the amplitude (the peak value) of the function is multiplied by -.

To find the value of $y$ for a given value of $x$ , we simply substitute the value of $x$ into the expression and calculate the result.
$y=-4 \cos (x)$

For example, let's find the value of $y$ when $x =0$ .
$y=-4 \cos (0)$

We know that $\cos(0) =1$ , so we substitute this into the expression.
$y=-4 \times1$

Calculate the value of $y$ .
$y=-4$ So when $x =0$ , $y = -4$ .

We know that $\cos(\pi/2) =$ , so we substitute this into the expression.
$y=-4 \times$

Calculate the value of $y$ .
$y=0$ So when $x = \pi/2$ , $y =0$ .