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Answer:
<em>41.8°, 138.2° and 401.8°</em>
Step-by-step explanation:
Given the expression;
Let P = sinx
The expression becomes;
3P²+4P - 4 = 0
Factorize
3P²+6P-2P - 4 = 0
3P(P+2)-2(P+2) = 0
3P-2 = 0 and P+2 = 0
P = 2/3 and -2
When P = 2/3
sinx = 2/3
x = arcsin 2/3
x = arcsin 0.6667
x = 41.8 degrees
Also if P = -2
sinx = -2
x = arcsin (-2)
x will not exist in this case
To get other values of x
sin is positive in the second quadrant
x = 180 - 41.8
x = 138.2°
x = 360+41.8
x = 401.8°
<em>Hence the values of x within the interval are 41.8°, 138.2° and 401.8°</em>