Calculus Question

Question

3 sin² x + 2 sin x = 1

One answer is

a. 0°

b. 90°

c. 270°

d. 180°

My answer is c

Another set of answers is

a. { 19° 28' , 340° 32'}

b. { 19° 28' , 160° 32'}

c. { 160° 32' , 199° 28' }

d. { 199° 28' , 340° 32' , }

My answer is b

Answer 1

This is a factoring problem but also with an understanding of trig:

3 sin²x + 2sinx = 1

3 sin²x + 2sinx – 1 = 0                                 Set the equation to zero

(3 sin x – 1)(sin x + 1) = 0                            Factor the equation

Solutions:

(3 sin x – 1) = 0                            or    (sin x + 1) = 0

sin x = 1/3                                     or     sin x = -1

x = 19.48° or 160.53°                  or     x = 270°

in DMS, x = 19°28’ or 160°32’    or x =270°

Your answers were correct!