Question

help me with some trig equations!

Answer 1

4sec(x)+6=-2
So I now you simplify this and then
sec(x)= 2
and I know that sec is 1/cos

Answer 2

Are we solving for "x"?

Answer 3

well we are just finding the solution to the equation. I am at the point where i need to look at the unit circle and fine out where sec(x)=2 I think

Answer 4

ok i have no idea if this is anywhere near the anwser but i want to say its sec(x)=-4?

Answer 5

hmmm I dont think so i think it is sex(x)=2 since -8/4 is 2

Answer 6

no wait it is sex(x)= -2

Answer 7

if sec(x)=-2 then cos(x)=-1/2

Answer 8

i dont know sorry

Answer 9

Yes i solved that one. @freckles can you help me with another one?

Answer 10

tan(x/2)=-1
I know that you can multipuly both sides by 2 to get
tan(x)=-2
but then where is tan(x)=-2 on the unit circle? what does that mean for sin and cos

Answer 11

u cannot do that

Answer 12

\(4 \sec x+6=-2\)

\(4 \sec x=-8\)

\(\sec x=-2\)

\(\dfrac{1}{\cos x}=-2\)

\(\cos x = - \dfrac{1}{2} \)

Answer 13

tan(x/2) is not the same as (tanx)/2

Answer 14

how can it not work? is it tan(x)=2 then?

Answer 15

Oh I see

Answer 16

it is tan x/2 = -1

Answer 17

Since tan x/2 = -1, solve for x/2.
What angle has a tan of -1?
Then write x/2 = that angle.
Now multiply both sides by 2 to find the angle.

Answer 18

I dont know which angle has a tan of -1

Answer 19

Remember that the tan is the sin/cos, right?

Answer 20

yes

Answer 21

I know that i just dont see where sin/cos=-1

Answer 22

You want to find angle A where the tan A = -1.
Just for a moment, ignore the negative sign.
If you were looking for where tan A = 1, since tan A = sin A/cos A,
since you want sin A/cos A = 1, that means the sine and cosine must be equal
so when you divide the sine by the cosine you get 1.

Answer 23

At what angle are the sine and cosine equal?

Answer 24

well let me see

Answer 25

\(\tan A = 1\),

but \(\tan A = \dfrac{\sin A}{\cos A} \),

so \(\dfrac{\sin A}{\cos A}= 1\)

A division equals one when you divide a number by itself.

Answer 26

I got it its 5pi/4

Answer 27

awesome

Answer 28

At 45 deg and any angle that has 45 deg as a reference angle, the tangent is either 1 or -1.

Answer 29

okay thats good to know then

Answer 30

I have another one
solve;
sin(x)sin(x)-1)=0

Answer 31

At 45 deg, the sine and cosine are equal.
Then, tan 45 = 1

Answer 32

Okay thanks @mathstudent55

Answer 33

In your case, remember we need the tangent to be =-1, not 1.
We still need to use 45 deg, but we need to see in which quadrants the sine and cosine are equal in number but opposite signs so sine/cosine = -1.

Answer 34

The graph above shows in which quadrants the sine, cosine and tangent are positive or negative.

Answer 35

gotcha

Answer 36

Since you have

tan A = -1, you need quadrants 2 and 4.

Answer 37

i see