Thread: Trigonometric Functions

The final line of my attempt contains the 2 answers listed in the book, but I'm not sure what the basis for excluding all the other values under is? I have a feeling my approach is slightly incorrect here. Can anyone help me clear this up?

Many thanks.

Q. Solve the equation for .

Attempt: . Sin is positive in the 1st & 2nd quadrants.
or
Since the angle is add & to each angle (i.e. & ):
or
or

Ans. (From text book):

It is odd that the stated interval for is given in radians, yet the roots are given in degrees. Anyway, we are told:

which means:



From the given equation, we find:

hence:

Ok, thank you. My only other question then is why, based on the 2 answer outcome to the problem in the first post, is the answer to the similar question of for shown as a three solution answer ?

Following, on from above I get:
. Cos is negative in the 2nd & 3rd quadrants.
or

How do I account for the 160?

With:



we have:



So, we find:

and so:

Ok, thank you.