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| PAGE: 491 | SET: Exercises | PROBLEM: 7 |
The trigonometric equation is 
in the interval 
.
.
From Pythagorean theorem,
The square of the hypotenuse is equal to sum the squares of the other two sides.
.
Where 
lies in first quadrant.
In first quadrant, the six trigonometric functions are positive.
.
(a)
Find 
.
Use Double-angle formula: 
.
Substitute 
and 
.
.
(b)
Find 
.
Use Double-angle formula: 
.
Substitute and .
.
(c)
Find 
.
Use Half-angle formula: 
.
Substitute .
Where 
lies in first quadrant, since 
lies in first quadrant.
.
(d)
Find 
.
Use Half-angle formula: 
.
Substitute .
Where 
lies in first quadrant, since lies in first quadrant.
.
(a) 
.
(b) 
.
(c) 
.
(d) 
.
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