SOLUTION: Given {{{ sinx=3/4 }}} and secx is less than 0, find cosx and tanx.
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Question 465237: Given and secx is less than 0, find cosx and tanx.
Found 2 solutions by solver91311, Ryan O:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Given:
\ =\ \frac{3}{4})
and
\ <\ 0)
But:
\ <\ 0\ \Leftrightarrow\ \frac{1}{\sec(x)}\ <\ 0\ \Leftrightarrow\ \cos(x)\ <\ 0)
Since:
\ =\ \frac{9}{16})
And since:
\ =\ 1\ -\ \cos^2(\varphi))
We can say:
\ =\ \frac{7}{16})
Which, coupled with the fact that \ <\ 0)
, leads us to deduce that:
\ =\ -\frac{\sqrt{7}}{4})
Then, since we know that \ =\ \frac{\sin(\varphi)}{\cos(\varphi)})
, we can write:
\ =\ \frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}}\ =\ \frac{3\sqrt{7}}{7})
John
My calculator said it, I believe it, that settles it
Answer by Ryan O(12) (Show Source): You can put this solution on YOUR website!
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