score: 90/150 answered: 10/15 × question 10 score on last try: 0 of 10 pts. see details for more. at least…

score: 90/150 answered: 10/15 × question 10 score on last try: 0 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question get a similar question you can retry this question below solve sin(x)=−0.64 on 0≤x<2π there are two solutions, a and b, with a < b a = b = give your answers accurate to 3 decimal places question help: post to forum submit question

score: 90/150 answered: 10/15 × question 10 score on last try: 0 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. > next question get a similar question you can retry this question below solve sin(x)=−0.64 on 0≤x<2π there are two solutions, a and b, with a < b a = b = give your answers accurate to 3 decimal places question help: post to forum submit question

Answer

Explanation:

Step1: Find the reference angle

We know that $\sin(x)=0.64$, then the reference - angle $x_{ref}=\sin^{-1}(0.64)$. Using a calculator, $x_{ref}\approx0.694$ radians.

Step2: Determine the solutions in the given interval

Since $\sin(x)= - 0.64<0$, the solutions are in the third and fourth quadrants. For the third - quadrant solution $A$: $A=\pi + x_{ref}=\pi+0.694\approx3.142 + 0.694=3.836$. For the fourth - quadrant solution $B$: $B = 2\pi-x_{ref}=2\pi - 0.694\approx6.283-0.694 = 5.589$.

Answer:

$A = 3.836$ $B = 5.589$