Question

I need help asap!! Will medal and fan!

Answer 1

Which of the following are solutions to the equation \[\sin x \cos x=-\frac{ 1 }{ 4 }\]

Answer 2

7pi/12 + npi/2

7pi/12 + npi

11pi/12 + npi

7pi/6 + npi

Answer 3

use the identity sin 2x = 2 sinx cosx

Answer 4

so we have

(1/2) sin 2x = -1/4
sin2x = -1/2

Answer 5

I'm still so confused ;-;

Answer 6

x=-1/2*sin2

Answer 7

you need to find angles whose sine = -1/2

Answer 8

7pi/12 + npi/2

7pi/12 + npi

11pi/12 + npi

7pi/6 + npi

You have just 3 unique values: 7pi/12, 11pi/12 and 7pi/6. Do any of these satisfy the given equation? This will help you to narrow down your choices.

Answer 9

substitute 7pi/12 for x in the given equation. Is the resulting equation now true or false? And so on.

Answer 10

Hint the sine is negative in 3rd and 4th quadrants

Answer 11

Thank you all so much ^.^ it makes a little more sense now.

Answer 12

What are the parts that are added to the end for?

Answer 13

You can't ignore those. Note that sine and cosine functions are periodic (they repeat themselves regularly). Having narrowed down your choices, now determine which "parts added to the end" are correct and which are not.

Answer 14

So they determine where the next solution will be?

Answer 15

yes

eg you might have a solution pi/2 + n pi

which means pi/2 , 3pi/2 , 5pi/d and so on..

Answer 16

THANK YOU SO MUCH

Answer 17

yw

Answer 18

\[\sin(x)=-1/(2cosx) \]

You can find this to be true by sin(2x) by the double angle formula and algebraic manipulation. Easiest way would be graphing and finding where the functions intersect.

Answer 19

Certainly that's another valid approach, but obtaining solutions from graphs accurately can be harder than finding them algebraically.