Sine and Cosine problems help?

Question

I need help with the following problems please help me solve it:

2. Solve 5sinx = -1 for 0
3. Solve 3 - 2cscx = 17 for 0
Thanks these problems are very confusing.

Answer 1

For both of these you'll need a scientific calculator or a sin table. The way to approach these is to solve it like you would a normal one-variable equation (like 2x + 1 = 5), but instead of getting x by itself, you're getting sin x or csc x by itself. Then, you need that calculator or the table to find out what x equals.

For the first one:

5sin x = -1
sin x = -1/5
sin x = -0.2

You could look up the value in the table where sin x = -0.2 and find the angle x, but that won't give you a precise answer. You could take your calculator and use its inverse sin function. How you do that depends on your calculator, but in some cases you just type -0.2, then INV, then SIN, and you should get -11.5 degrees. But since your answer has to be between 0 and 360, just add 360 to this to get 348.5 degrees (adding or subtracting 360 to an angle gives you an equivalent angle).

The second problem is the same:

3 - 2csc x = 17
-2csc x = 14
csc x = -7

Your calculator more than likely doesn't have a csc function, but csc is the inverse of sin, so:

csc x = -7
sin x = -1/7

And you can use the same procedure here that you used above. Calculating, you should get -8.21 degrees, and adding 360 gives you 351.79. To convert to radians, multiply by pi and then divide by 180, and you should get 6.14 rad. (Alternatively, your calculator may be able to calculate in radians - look for a MODE button that should change your calculations from DEG to RAD to GRAD or something like that.)