Trigonometric equations

[grim glacier]

so i will explain 2nd

do you know general values of sin eqn

[real thicket]

nope

[grim glacier]

wait

$sin \alpha = sin \beta \implies \alpha = n\pi + (-1)^n \beta$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[real thicket]

what does this mean

[grim glacier]

where n = integer

its a general solution

for sin

[real thicket]

sure

and how do I solve the equation

[grim glacier]

so our question is

$sin (3x + \pi) = \frac{\sqrt3}{2} = sin{\frac{\pi}{3}}$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[real thicket]

so you converted the right side to sin right?

[grim glacier]

yes

[real thicket]

ok

[grim glacier]

for cos

[real thicket]

what

[grim glacier]

$cos \alpha = cos \beta \implies \alpha = 2n\pi \pm \beta$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[grim glacier]

where n = integer

[real thicket]

can you explain how did you use this

[grim glacier]

ok

so take the second question

[grim glacier]

this

$3x + \pi = n\pi + (-1)^n \frac{\pi}{3}$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[grim glacier]

now take n = 0

3x + pi = pi/3

3x = 2pi / 3

x = 2 pi/9

now 1

3x + pi = pi - pi/3

3x = -pi

x = -pi/9

or you can write

$x = \frac{(n-1)\pi + (-1)^n \frac{\pi}{3}}{3}$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[real thicket]

oh I see

and that is the solution for it right?

[grim glacier]

yes

for n = integer

mention this

[real thicket]

and how do you decide what to plug in instead of n

[grim glacier]

any integer

n = -1 or 0 or 5

anything

one by one

[grim glacier]

same with this

[real thicket]

so you first did 0 why wasnt that enough

then you did 1

[grim glacier]

just to tell you that infinite solutions exist

so we use general solution

otherwise you can use direct method

3x + pi = pi/3

3x = -2 pi /3

x = -2 pi /9

[real thicket]

i think i need to do the general one

[grim glacier]

ok

so for tan

$tan \alpha = tan \beta \implies \alpha = n\pi + \beta$

[tribal wharf]

ᴰᴱᴬᴰ ★ ᴋɪʟʟᴇʀ ⁰⁴

[grim glacier]

remember these three formulae

[real thicket]

sure

btw what level math do you think is this

[grim glacier]

of 11th standard

in india at least

[real thicket]

alright, thanks, i'll try to process it lol

[grim glacier]

ok

[real thicket]

how do i convert sqrt(3)/2 to sin(pi/3)?

is there a way to do that on a calc or ?

[grim glacier]

its direct value

[real thicket]

am i supposed to know that that equals that?

oh yeah i found it using the inverse function on the calc

solution for the first one is

x = n*pi+-pi/4 ?

where n is integer

i hope i did it correctly

@grim glacier

[grim glacier]

yes

[real thicket]

cool, ill just keep solving them and writing the solution here

[grim glacier]

ok

general

or direct

[real thicket]

general im pretty sure that's what i need

direct is too easy

[grim glacier]

ok

[real thicket]

.close