Question

solve for the principal values of indicated variable: 2sin(2x)-sqrt3=0
and
tan^(2) x-1=0

Answer 1

ok: \[\sin(2x)=\frac{1}{2}\sqrt{3}\]

Answer 2

When is the sine 1/2sqrt(3)?

Answer 3

please clarify?

Answer 4

For what value(s) of x does sin(x) equal \[\frac{1}{2}\sqrt{3}\]?

Answer 5

60 degrees

Answer 6

[pi/3]

Answer 7

Is that the only solution?

Answer 8

2pi/3

Answer 9

right, additionally you can add multiples of 2pi to those solutions.

Answer 10

so 2pi+(1/3)pi is also a solution.

Answer 11

ok so what about the sin2x does the 2 not matter?

Answer 12

it does matter, we're not done yet.

Answer 13

2x=1/3pi, 2x= 2/3pi

Answer 14

Let's be a bit more precise
2x=1/3pi +k*2pi OR 2x=2/3pi+k*2p
for any constant k.

Answer 15

got it thanks!
can you help me with the second question:\[\tan ^{2}X -1=0\]?

Answer 16

ok, \[\tan^2(x)=1\]

Answer 17

ok what next sensei?

Answer 18

we need to get rid of the square of course.

Answer 19

do we do that by changing it to 1-cos2X
-------
1+cos2x
or is there an easier way?

Answer 20

tan^2(x)=tan(x)^2, so tan(x)=?

Answer 21

wait, let's do this first: x^2=1, what's x?

Answer 22

1

Answer 23

is that all?

Answer 24

-1?

Answer 25

right, (-1)^2=1

Answer 26

so what does tan(x) equal?

Answer 27

1 or -1?

Answer 28

right, so we have tan(x)=1 OR tan(x)=-1

Answer 29

ok

Answer 30

when does tan(x) equal 1?

Answer 31

pi/4 or 5pi/4

Answer 32

or 9pi/4,or...
this is the same as before, now you can add a multiple of pi to the answers.

Answer 33

got it thanks!!

Answer 34

You're welcome, you still need to do the tan(x)=-1 of course.

Answer 35

yes 3pi/4 ect right?

Answer 36

right.

Answer 37

thank you