Solve the Trigonometric equation for all solutions between [0,360)degrees.

Sinx + 1 = 2.6635

Please, Please, Please Help Me!!!!!!!!!!

I know it's trig, but could you please help me to solve the problem.

Since sin(x) is never greater than 1, there is no value of x where sin(x)+1 > 2

To solve the trigonometric equation sin(x) + 1 = 2.6635, we can start by subtracting 1 from both sides:

sin(x) = 2.6635 - 1
sin(x) = 1.6635

To find the solutions, we need to take the inverse sine (or arcsin) of both sides of the equation. However, it is important to note that the arcsin function gives us a range of values between -90° and 90°.

arcsin(sin(x)) = arcsin(1.6635)

Now, we need to find the inverse sine (or arcsin) of 1.6635. However, if we directly substitute this value into a calculator, we might not get the correct solution because the calculator will only provide the principal value (between -90° and 90°) of the inverse sine.

To find all solutions between [0, 360) degrees, we need to use the symmetry of the sine function. The sine function is positive in the first and second quadrants. This means that if sin(x) = 1.6635, then sin(180 - x) = 1.6635 as well.

So, we have two possible equations:

1) sin(x) = 1.6635
2) sin(180 - x) = 1.6635

To solve the first equation, we can take the inverse sine of 1.6635:

x = arcsin(1.6635)

Substituting this value into a calculator, we find x ≈ 61.99°.

To solve the second equation, we can subtract the value of x we found from 180:

180 - x ≈ 180 - 61.99 ≈ 118.01°

Therefore, the solutions to sin(x) + 1 = 2.6635 between [0, 360) degrees are approximately x ≈ 61.99° and x ≈ 118.01°.