trig equations

[hardy agate]

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[hushed field]

put tan^2=sec^2-1

and solve the quadratic

but answer should be more than 1 or less -1

@warped zenith

[warped zenith]

ty

$-4+3sec^2\theta+4sec\theta =0$

[stiff isle]

Goose

[warped zenith]

sub sec\theta for u:
\newline
\newline
$3u^2+4u-4=0$

[stiff isle]

Goose
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[warped zenith]

u=2/3
u=-2

$\theta= sec^{-1}(2/3)$
$\theta= sec^{-1}(-2)$

[stiff isle]

Goose

The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)

[warped zenith]

okay what now

[hushed field]

well arcsec 2/3 is not defined

and arcsec(-2) has 2 values of theta

$2\pi/3$ and $4\pi/3$

[stiff isle]

scilent

[warped zenith]

yeah i got that far

i mean i forget what i add to the values when its arcsec

like the quadrants

if you know what i mean

[hushed field]

you mean like sign?

[warped zenith]

yeah

dont these questions have
the theta values +90, +180 or +360

[hushed field]

its same as for cos

since sec =1/cos

[warped zenith]

ahh right

[warped zenith]

so theta values +270

?

[hushed field]

no

+180 or 180-theta

[warped zenith]

+180 because of the range

[warped zenith]

oh right

that too

so 6 answers

got it

thank you so much

[hushed field]

what? no

2 answers

[hushed field]

these 2

[warped zenith]

thats it?

[hushed field]

yeah

since its between 0 and 360 degrees

[warped zenith]

just verifying i got the right answers:
\newline
$2\pi/3$
\newline
$2\pi/3 +180$
\newline
$180-2\pi/3$
\newline
$4\pi/3$
\newline
$4\pi/3+180$
\newline
$180-4\pi/3$

[stiff isle]

Goose

[hushed field]

2pi/3 + 180 is more than 360

[hushed field]

180-2pi/3

is pi/3

thats wrong

[stiff isle]

scilent

[warped zenith]

ohhh

that makes perfect sense

[warped zenith]

thanks very much

[last oasis]

@warped zenith has given 1 rep to @hushed field

[warped zenith]

+close