trigonometry equation, solve exactly.

Question

solve exactly:

sin^2(x)-cox(2x)=(-1/4)

 

Answer 1

sin^2(x)-cos(2x)=-1/4

cos(2x)=1-2sin^2(x)  (trig identity)

substitute

sin^2(x)-(1-2sin^(x))=-1/4

sin^2(x)-1+2sin^2(x)=-1/4

3sin^2(x)-1=-1/4

3sin^2(x)=1-(1/4)

3sin^2(x)=3/4

multiply both sides by (1/3)

sin^2(x)=1/4

take the square root of both sides

√sin^2(x)=√1/4

sin(x)=±(1/2)

sin(x)=1/2

x=∏/6=30º looking on the unit circle or a table or arcsin on your calculator

sin(x)=-1/2

x=7∏/6=210º from the unit circle or a table or a calculator