Cos ( α ) = 11/8 and sin ( β ) = √ 7/5 . Find cos ( α + β )

Step-by-step explanation:

We are given that:

Where both α and β are in QI.

And we want to find cos(α + β).

First, let's determine the side lengths for each angle.

For α, we are given that its cosine is √(11)/8.

And since cosine is the ratio of the adjacent side to the hypotenuse, the adjacent side to α is √11 and the hypotenuse is 8.

Therefore, the opposite side will be:

Hence, for α, the adjacent side is √11, the opposite side is √53, and the hypotenuse is 8.

Likewise, for β, we are given that its sine is √7/5.

And since sine is the ratio of the opposite side to the hypotenuse, the adjacent side of β is:

In summary:

For α, the adjacent is √11, the opposite is √53, and the hypotenuse is 8.

For β, the adjacent is 3√2, the opposite is √7, and the hypotenuse is 5.

Using an angle addition identity, we can rewrite our expression as:

And since both α and β are in QI, all trig ratios will be positive.

Using the above information, we can substitute in the following values:

Finally, simplify:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

kk.bj.

step-by-step explanation:

.mnm.kn.kj