Edwin's solution:
a) and
The sine is positive and the cosine is negative
only in quadrant II
To find :
<-- fundamental identity to use
But we are given that
so we choose the negative answer for ,
therefore:
------------------
To find :
<-- fundamental identity to use.
------------------
To find
<--- fundamental identity to use
-------------------
To find
<--- fundamental identity to use
==================================================
b) ,
Sorry this is a mistake because and
cosines are always between and .
So if you didn't copy it wrong, then there
is no solution!
=================================================
c) ,
The tangent is negative and the sine is positive
only in quadrant II
To find :
<-- fundamental identity to use
But since this is in Quadrant II, the secant, which
is the reciprocal of the cosine, is negative, we choose
the negative answer for , therefore:
------------------
To find :
<-- fundamental identity to use.
------------------
To find :
<-- fundamental identity to use
But we are given that
so we choose the positive answer for ,
therefore:
-------------------
To find
<--- fundamental identity to use
-------------------
To find :
<-- fundamental identity to use.
==================================================
d) ,
The tangent is positive and the sine is positive
only in quadrant I, so all trigonometric ratios are
positive:
To find :
<-- fundamental identity to use
But since this is in Quadrant I, all trig rations are
positive therefore:
------------------
To find :
<-- fundamental identity to use.
------------------
To find :
<-- fundamental identity to use
But we are given that
so we choose the positive answer for ,
therefore:
-------------------
To find
<--- fundamental identity to use
-------------------
To find :
<-- fundamental identity to use.
-------------------------------
e) , sinx>0
The cotangent is positive and the sine is positive
only in quadrant I, so all trigonometric ratios are
positive:
To find :
<-- fundamental identity to use
But since this is in Quadrant I, all trig ratios are
positive therefore:
------------------
To find :
<-- fundamental identity to use.
------------------
To find :
<-- fundamental identity to use
But we are given that
so we choose the positive answer for ,
therefore:
-------------------
To find
<--- fundamental identity to use
-------------------
To find :
<-- fundamental identity to use.
=====================================================
f)
You didn't give enough information, as you need to be
given that another trig ratio is >0 or <0.
Edwin