Question

Find all radian measures of A.
(2sinAcosA)^2+4sin2A-1=0

Answer 1

use

\(\large \color{black}{\begin{align}2\sin a \cdot \cos a=\sin 2a\hspace{.33em}\\~\\
\sin2a=x\hspace{.33em}\\~\\
\end{align}}\)


then solve the quadratic

Answer 2

Do I plug in 2sina*cosa in to sin2a?

Answer 3

substitute first
\(\large \color{black}{\begin{align}
\sin2a\hspace{.33em}\\~\\
\end{align}}\)
for


\(\large \color{black}{\begin{align}
2\sin a\cdot \cos a\hspace{.33em}\\~\\
\end{align}}\)

Answer 4

i did that. I got (sin2A)^2+4sin^2A-1=0

Answer 5

ok now substitute \(x\) for \(\sin 2a\)

Answer 6

ok I did, then what do I do?

Answer 7

you will get this equation


\(\large \color{black}{\begin{align}
x^2+4x-1=0\hspace{.33em}\\~\\
\end{align}}\)

u can now apply the quadratic formula to find \(x\) or use completing the square method

Answer 8

so after using the quadratic formula i got 0.23 radians and 2.9 radians

Answer 9

but the correct answer is 0.12 and 3.02

Answer 10

after solving the quadratic you will get

you will get this equation
\(\large \color{black}{\begin{align}
x=0.23\hspace{.33em}\\~\\
x=-4.23\hspace{.33em}\\~\\
\end{align}}\)

now substitute back

\(\large \color{black}{\begin{align}
\sin 2a=x\hspace{.33em}\\~\\
\end{align}}\)

Answer 11

ok thank you