How do i demonstrate that there is only one value of x (between 0 and 2pi) that verifies cosx=3/5 and sinx=4/5

well, as we can see, the cos(x) as well as the sin(x) are both positive, that puts the angle in the I Quadrant only, everywhere else they differ in signs or are both negative.

that simply means it has an adjacent side of 3, opposite side of 4, and a hypotenuse of 5, like you see it in the picture below.

and we can get the inverse function of either function to get about 53.130102354° for ∡x.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11