00:01
This problem wants us to select one or more expressions that together represent all solutions to the equation, and our answer should be in degrees, assuming n is any integer, and we're given 8 times sine of 8x plus 9 equal to 3.
00:12
And we're not given the expressions to choose from, but what we can't do is come up with two expressions to represent our solutions here.
00:18
And to start off solving, we need to isolate sine of 8x, and we'll do that by first subtracting 9 from both sides, which will give us 8 times sine of 8x equal to 3 minus 9 or negative 6.
00:30
And then we'll divide both sides by 8 to give us sign of 8x equal to negative 6 .8s, which would simplify to negative 3 .4s.
00:39
And now, making sure our calculator is in degree mode, we'll take inverse sign of both sides of the equation.
00:46
And that will tell us that the angle, in this case, 8x, is equal to inverse sign of negative 3 .4s, which rounded to 2 decimal places, gives us negative 48 .5 .9 degrees.
00:59
And to get this into its positive representation to start off writing our solution, we will add 360 degrees to get a coterminal angle, which gives us our first solution of 311 .41 degrees.
01:14
And with sine being equal to a negative value, that means we would have two solutions...