Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve $4 {sin}^{2} x + 1 = - 4 sin x$ $4sin^2x + 1 = -4sin x$ ?

1 Answer

Jul 22, 2015

$x = \frac{π}{6} + k \cdot 2 π$ $x= pi/6 +k*2pi$
or
$x = \frac{5 π}{6} + k \cdot 2 π$ $x= (5pi)/6 + k*2pi$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ for all $k epsilon ZZ$

Explanation:

$4sin^2(x) + 1 = 4 sin(x)$

$rArr 4sin^2(x)-4sin(x)+1=0$

$rArr (2sin(x)-1)^2 = 0$

$rArr 2sin(x) = 1$

$rArr sin(x) = 1/2$

If we limit the range of $x$ to $[0,2pi]$
the above represents a standard trigonometric triangle with
$color(white)("XXXX")$ $x = pi/6 or (5pi)/6$

Related questions

See all questions in Solving Trigonometric Equations

Impact of this question

9656 views around the world

You can reuse this answer
Creative Commons License