Find the exact value of the angle in radians and justify your answer.
I'm stuck on this one why can't I just use the arctan function on my calculator? I know I can't that would be too simple. Can any one give me a clue ?
Well, cos = 1/sec so we have that , which leads us to which implies that . Where in do we find such an angle? is the only one I can think of.Originally Posted by macca101
The reason that just taking the inverse tangent won't work is that you will get a list of possibles and the answer is buried in there. However, you could do the inverse tangent and inverse secant and compare the two lists...(rather like what I did with the sine and cosine values.)
-Dan
There are some anlges that you need to have remorzied to be able to answer this question.Originally Posted by macca101
Notice that,
Thus,
That happens, when -memorized.
Notice that,
happens when -memorized.
But, problem ask for
Thus, since
We have that
Hi:
In evaluating arctan [-sqrt(3)], your calculator will provide a decimal approximation to the tune of -1.0471975511 ± a few decimal places. But the problem is specific in calling for an EXACT value of theta which, as it happens, is irrational and therefore with infinitely many non-repeating digits to the right of the decimal point. And this is why you are well advised by PHckr, to commit exact trigonometric values of certain key angles to memory.
Regards,
Rich B