Answer:
The answer is B and C
Step-by-step explanation:
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Let


because that is the range of the inverse cosine funcition.
Also,
![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3Dcos%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B5%5C%2Ccos%5C%2C%5Ctheta%3D4%7D)
Square both sides and apply the fundamental trigonometric identity:



But

which means

lies either in the 1st or the 2nd quadrant. So

is a positive number:
![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Ctherefore~~%5Cmathsf%7Bsin%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%3D%5Cdfrac%7B3%7D%7B5%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
Answer:
Step-by-step explanation:

Subtract 4 times the first equation from the second:
(-7y +16x -80) -4(-9y +4x -20) = (0) -4(0)
29y = 0 . . . . . simplify
y = 0 . . . . . . . .divide by 29
4x -20 = 0 . . . . substitute 0 for y in the first equation
x -5 = 0 . . . . . .divide by 4
x = 5 . . . . . . . . add 5
The solution to this system is (x, y) = (5, 0).
Start by multiplying 15 by 5, and you get 75. then subtract that from 82, and you get 7. Since you are below the surface, the number is negative. So you get -7.