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## Trigonometry equations

I know this may be a very informal question but I want to know the difference between these two types of questions.

Find solutions between 0 and 2pi to the following equations

a) 4 sin (x) + 2 = 6
sin(x) = pi/2
Sin is positive in Quadrant 1 and 2
therefore,
x = pi/2, pi - pi/2
x = pi/2

b) sin (x/3) + 5 = 5.32
sin (x/3) = 0.32
x = 0.32 x 3 = 0.96

OK - so this is my question. For question A, my answer was an exact value, so does that mean I need to consider what quadrant it is in and find it's equivalent angle? On the other hand, 0.32 is not an exact value and thus I wouldn't need to find it's equivalent angles? And that's why they just solved for x straight out?

Sorry if this question is really confusing but I can't really explain my problem! It's just that these two questions are solved differently because one is an exact value and the other one isn't (0.32) and I just want to know why. Thanks!

This line: sin(x/3) = 0.32 => x = 0.32 * 3 = 0.96 is absolutely wrong!!!

It's like the sine function just disappeared into x/3 = 0.32

The only reason why it looks like this is the way they have done it is because sin(0.32) is approximately 0.32. That is a complete coincidence.

The way you need to solve it is just like the above, except you use the calculator to get the number instead of the exact values.

sin(x/3) = 0.32
=> x/3 = arcsin(0.32) = 0.325729...
=> x = 0.977187

For your information, arcsin is the same as inverse sine or sin^(-1) on your calculator.

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