Asked by Dave
How do you solve
sin x * cos x = 1/4
I don't know where to start.
sin x * cos x = 1/4
I don't know where to start.
Answers
Answered by
Reiny
An important identity is
sin (2x) = 2sinxcosx
so if
sinx cosx = 1/4
2sinx cosx = 1/2
sin (2x) = 1/2
2x = 30° or 2x = 150°
x = 15° or x = 75°
since the period of sin (2x) = 360°/2 or 180°,
other solutions are 15+180 or 195°
and 75+180 or 255°
in radians: π/12, 5π/12, 13π/12, and 17π/12
testing one of them:
sin 195° * cos 195° = .25 , looks good
sin (2x) = 2sinxcosx
so if
sinx cosx = 1/4
2sinx cosx = 1/2
sin (2x) = 1/2
2x = 30° or 2x = 150°
x = 15° or x = 75°
since the period of sin (2x) = 360°/2 or 180°,
other solutions are 15+180 or 195°
and 75+180 or 255°
in radians: π/12, 5π/12, 13π/12, and 17π/12
testing one of them:
sin 195° * cos 195° = .25 , looks good
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.