Question

use an identity to solve the equation on the interval [0,2pi) sin x cos x = -1/4 x=

Answer 1

Answer:

The solution of the given equation is    x = 105 °∈ ( 0 , 2pi)

Step-by-step explanation:

Step(i):-

Given equation is sin x cos x = -1/4

                           $2(2sinxcosx) = -1$

we know that trigonometry formula

                             2 sin x  cos x = sin 2x

                            2 ( sin 2 x) = -1

                                sin2x = -1/2

Step(ii):-

                            sin2x =    $\frac{-1}{2} = sin (\pi +\frac{\pi}{6}$

                 sin2x = sin 210

                      2x = 7π/6

                      2x = 210°

                               x = 105 °

The solution of the given equation is    x = 105 °∈ ( 0 , 2pi)