Question

what are the values for: theta( 0<= theta <= 2pi) satisfy the equation?
2 sin theta cos theta + sqrt 2 cos theta = 0

Answer 1

Any idea?

Answer 2

not much i'm really confused with this question

Answer 3

how do you feel about factoring?

Answer 4

i know one of them is pi/2 and i think another is 3pi/2

Answer 5

i'm okay with it

Answer 6

try it on your left hand expression

Answer 7

huh?

Answer 8

the pronoun was to stand for factoring

Answer 9

if you can see both terms on the left expression have a common factor of cos(t)
then you should be able to factor that left hand expression
bringing out the common(then putting here the leftovers)=0

Answer 10

so 2 sin theta + sqrt 2=0?

Answer 11

\[\cos(t)(2 \sin(t)+\sqrt{2})=0\]
yep that is one equation
you also have cos(t)=0

Answer 12

okay so where am i supposed to go from there?

Answer 13

cos(t)=0 can be solved using unit circle
sin(t)=-sqrt(2)/2 can also be solved using unit circle

Answer 14

i'm not really sure what those are

Answer 15

ok let's look at solving cos(t)=0
this means look at your circle and find the angles for which x coordinate is 0

Answer 16

the x-coordinate is the first number in an ordered pair

Answer 17

you will solve sin(t)=-sqrt(2)/2 in a similar wy
on the unit circle the y-coordinate is the sine value
look for what angles the y-coordinate is -sqrt(2)/2

Answer 18

the y-coordinate is the second number in an ordered pair

Answer 19

an ordered pair looks like (x , y)

Answer 20

https://www.mathsisfun.com/geometry/images/circle-unit-radians.gif

do you see we can solve sin(t)=-sqrt(2)/2
by looking in the 3rd and 4th quadrants? because that were the y value is negative?

Answer 21

cos(t)=0
can be solved by looking at the y-axis

Answer 22

i don't have any physical graphs or circles though? or should i have sketched one?

Answer 23

i think i figured it out? would the answer be pi/2, pi/4. 3pi/2, 11pi/4?

Answer 24

sin(pi/4)=sqrt(2)/2
and you want -sqrt(2)/2
11pi/4>2pi so that isn't even in the interval in which you were asked to solve

you are dead on about pi/2 and 3pi/2
cos(pi/2)=0
and
cos(3pi/2)=0

Answer 25

did you look at the unit circle
and look at the 3rd and 4th quadrants yes to find the angles for which y is -sqrt(2)/2?

Answer 26

7pi/4 is another then

Answer 27

yes

Answer 28

7pi/4 is in the 4th quadrant and yes sin(7pi/4)=-sqrt(2)/2
there is also an answer to sin(t)=-sqrt(2)/2 in the third quadrant

Answer 29

i'm not sure if the second quadrant is 3pi/4 or 5pi/4?

Answer 30

after you find that solution there are 4 total solutions to
2 sin theta cos theta + sqrt 2 cos theta = 0
in the interval [0,2pi]

Answer 31

well can you tell where y is negative?

Answer 32

you are looking for when sin(t)=-sqrt(2)/2
that means you only need to look in quadrants 3 and 4
because that is where sin is negative

Answer 33

I know the first quadrant is pi/2, i think the second is 5pi/4, the third is 3pi/2, and the fourth is 7pi/4. at least i think those are the answers

Answer 34

see in these two quadrants sin(t)=-sqrt(2)/2