Mathematics: Using the unit circle, determine the value of cos(945°).

9. Step-by-step explanation:We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet. First of all we will convert dimensions of poster from feet to inches.Now let us compare sides of our original photo with corresponding sides of poster. Now let us compare the second pair of corresponding sides. We have seen that sides of poster are 9 times the sides of our original photo, therefore,...

Using the unit circle, determine the value of cos(945°).

Ответ:

sarahmolina246

30.01.2022

Mathematics

Using the periodic property of cos function, you can evaluate the value of cos(945°).

The value of cos(945°) is given by:

$cos(945^\circ) = -\dfrac{1}{\sqrt{2}}$

Given that:To find the value of cos(945°) using the unit circle.What are periodic functions?

A function returning to same value at regular intervals of specific length(called period of that function).

What is the period of cosine function?

It is $2\pi$

Thus, we have:

$cos(x) = cos(2\pi +x) \: \forall \: x \in \mathbb R$

Using the periodic property of cosine:

$cos(945^\circ) = cos(2 \times 360^\circ + 225^\circ) = cos(2\pi + 2\pi + 225)\\
cos(945^\circ) = cos(2\pi) + 225) = cos(225^\circ)$

There is a trigonometric identity that:

$cos(\pi + \theta) = -cos(\theta)$

Thus:

$cos(945^\circ) = cos(225^\circ) = cos(180^\circ + 45^\circ) = -cos(45^\circ) = -\dfrac{1}{\sqrt{2}}\\
cos(945^\circ) = -\dfrac{1}{\sqrt{2}}$

Note that wherever i have used $\pi$ , it refers to $\pi ^ \circ$ (in degrees).

Thus, the value of cos(945°) is given by:

$cos(945^\circ) = -\dfrac{1}{\sqrt{2}}$

Learn more about periodicity of trigonometric functions here:

link

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Ответ:

ginger87771

30.01.2022

Mathematics

Choice B. $-\frac{\sqrt{2}}{2}$

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Explanation:

The angle 945 degrees is not between 0 and 360. We need to adjust it so that we find a coterminal angle in this range. To do this, subtract off 360 repeatedly until we get into the right range

945 - 360 = 585, not in range, so subtract again

585 - 350 = 225, we're in range now

Since 945 and 225 are coterminal angles, this means cos(945) = cos(225)

From here, we use the unit circle. Your unit circle should show the angle 225 in quadrant 3, which is the lower left quadrant. The terminal point here at this angle is $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$

The x coordinate of this terminal point is the value of cos(theta). Therefore $\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}$ and this is also the value of cos(945) as well

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Ответ:

ShianHagen5

10.03.2023

Mathematics

Step-by-step explanation:

We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.

First of all we will convert dimensions of poster from feet to inches.

$3\text{ feet}=3\times 12 \text{ inches}=36\text{ inches}$