Question

which of the following is a solution to 4sin^2x-1=0
a. 30 degrees
b. 60 degrees
c. 90 degrees
d. 120 degrees

Answer 1

Hello from MrBillDoesMath!

Answer:   a. 30 degrees

Discussion:

To solve  4 (sinx)  ^2  - 1 = 0 add 1 to each side:

4 (sinx)^2 = 1.                    Divide each side by 4:

(sinx)^2 = 1/4                     Take the square root of each side

sinx = 1/2

One solution to this equation is x = 30 degrees (choice a)

Thank you,

MrB

Answer 2

$4\sin^2x-1=0\qquad\text{add 1 to both sides}\\\\4\sin^2x=1\qquad\text{divide both sides by 4}\\\\\sin^2x=\dfrac{1}{4}\to\sin x=\pm\sqrt{\dfrac{1}{4}}\\\\\sin x=-\dfrac{1}{2}\ \vee\ \sin x=\dfrac{1}{2}\\\\\sin x=-\dfrac{1}{2}\to\ x=210^o+360^on\ or\ x=330^o+360^on\qquad n\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=30^o+360^on\ or\ x=150^o+360^on\qquad n\in\mathbb{Z}\\\\Answer:\ \boxed{a.\ 30\ degrees}$