Given:
There are given that the cos function:
Explanation:
To find the value, first, we need to use the half-angle formula:
So,
From the half-angle formula:
Then,
Since 105 degrees is the 2nd quadrant so cosine is negative
Then,
By the formula:
Then,
Put the value of cos210 degrees into the above function:
So,
Final answer:
Hence, the value of the cos(105) is shown below:
a.) A flat pattern that could be folded to make a 3-dimensional figure is called a "net." You can draw one for Tyler's bench by picking any surface of that rectangular prism and making a drawing of it. At any edge you choose, you can add the adjacent surface to your drawing. Keep doing this until all 6 surfaces are shown in their correct relationship to adjacent surfaces. An example is attached. (This is not the only way the net can be drawn.)
Interior lines of the net can be solid or dashed as you wish. I have shown some of them dashed so as to better illustrate how the area can be computed.
b.) The area of this figure represents the surface area of the rectangular prism. The dimensions of each surface will be 1×1.5, 1×5, or 1.5×5. There are two surfaces with each pair of dimensions. (Perhaps you can find each of these rectangles on the net diagram. Ones with the same dimensions are opposite faces of the rectangular prism.) We can add up the areas of the smaller rectangles to find the total, or we can take advantage of the drawing and divide the area into a smaller number of larger chunks that may make the computation easier.
For example, the rectangle AI that is shaded red is 5×4 in size, for a total of 20 ft². The rectangle KN that is shaded green is 8×1 in size, for a total of 8 ft². Then the total amount of cloth Tyler needs to reupholster his bench is
... 20 ft² + 8 ft² = 28 ft²
