Question

HELP QUICK PLEASE!!!!

Answer 1

41.8°, 138.2° and 401.8°

Explanation:

Given the expression;

`3sin^2x + 4sinx - 4 = 0`

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°

Hence the values of x within the interval are 41.8°, 138.2° and 401.8°