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| PAGE: 340 | SET: Exercises | PROBLEM: 12 |
The trigonometric equation is 
and the interval is 
.
Consider .
.
The general solution of 
is 
, where 
is an integer.
Divide each side by 2.
.
General solution is 
, where 
is an integer.
Find the angle in the interval 
.
General solution is , where is an integer.
If 
, 
.
If 
, 
.
If 
, 
.
If 
, 
.
Thus, the solutions are 
, 
, 
and 
in the interval .
Check graphically :
The trigonometric equation is .
Rewite the equation as 
.
Draw a coordinate plane.
Graph the equation 
in the interval .
Graph :
Observe the graph of the function :
The graph touches the x - axis at 
, 
, 
and 
.
Convert the angles from radians to degrees.
Thus, the solutions are , , and in the interval .
The solutions are , , and in the interval .
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