Question

solve the given equation to approximate the angle x. [0,pi/2) is the interval. Round to three decimal places: 75sin^2x - 34sinx+ 3 = 0

Answer 1

(25sinx-3)(3sinx-1)=0
sinx=3/25 and sinx=1/3

after that, you should a calculator to find the answer.

Answer 2

Oh wow alright that really helped! Thank you! :)

Answer 3

welcome :)

Answer 4

We put :
\[t=\sin x\]
Then, the equation becomes :
\[75t^2-34t+3=0\]
and :
\[\Delta=34^2-4\times75\times 3=256=16^2>0\]
So :
\[t_1=\frac{34+16}{2\times75}=\frac13\\
t_2=\frac{34-16}{2\times75}=\frac{3}{25}
\]
So :
\[\sin x=\frac13\Rightarrow x=0.34+2k\pi\text{ or }x=(\pi-.34)+2k\pi
\\\sin x=\frac3{25}\Rightarrow x=0.12+2k\pi\text{ or }x=(\pi-.12)+2k\pi
\]

Answer 5

thank you :) @Noura11