Question

PLZ HELP ME!
Which of the following are solutions to the equation sinx cosx = -1/4? Check all that apply.

A. 7pi/12+npi/2
B.7pi/12+npi
C.7pi/6+npi
D.11pi/12+npi

Answer 1

@jim_thompson5910

Answer 2

Look on page 2 of

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

where it says "Double Angle Formulas"

do you see where it has \(\Large \sin(2\theta)\) ?

Answer 3

Yes I do :)

Answer 4

what is it equal to?

Answer 5

2sin(theta)cos(theta)

Answer 6

if we isolate the `sin(theta)cos(theta)` part, we get

\[\Large \sin(\theta)\cos(\theta) = \frac{1}{2}\sin(2\theta)\]

Answer 7

agreed? or no?

Answer 8

I think so...im not very good at this...sorry

Answer 9

all I did was multiply both sides by 1/2

Answer 10

oh!! Okay...so how would i apply this to my answers?

Answer 11

do i divide them or something?

Answer 12

so `sinx cosx = -1/4` turns into `(1/2)*sin(2x) = -1/4`
agreed? or no?

Answer 13

one sec plz...sorry im taking long, computer is slow

Answer 14

that's fine

Answer 15

um...i guess it looks right...

Answer 16

now isolate the `sin(2x)` to get

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

when is sin(theta) = -1/2 true? for what theta value?

look at this unit circle

https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png

Answer 17

there are 2 such theta values

Answer 18

So...i kinda get it...kinda...so where do i go from here knowing these two values?

Answer 19

what two theta values did you get?

Answer 20

i solved and figured it out and got-------> 7pi/12+npi and 11pi/12+npi
Thx for starting me off!!

Answer 21

@jim_thompson5910

Answer 22

very good

sin(2x) = -1/2
2x = 7pi/6 + 2pi*n or 2x = 11pi/6 + 2pi*n
(1/2)*2x = (1/2)*(7pi/6 + 2pi*n) or (1/2)*2x = (1/2)*(11pi/6 + 2pi*n)
x = 7pi/12 + pi*n or x = 11pi/12 + pi*n