Radians

[sick elbow]

<@&791435371564892232>

@silent sigil

[silent sigil]

hello

[sick elbow]

ty

[silent sigil]

do you know the small angle approximations?

[sick elbow]

erm not really if u can explain i'll remember quickly

havent done thus chapter in a min and i have a test tomorrow 😂

[silent sigil]

basically cos(x)≈1-(x^2/2)
sin(x)≈x
tan(x)≈x
for small values of x, measured in radians

they come from the maclaurin expansions if you want to look into it further but that won't matter for a level normal maths

[silent sigil]

so you just use these approximations instead of sine and cosine

[sick elbow]

okay so i just sub those in

wait ill try

[silent sigil]

yes

[sick elbow]

what do i do about the 2 theta infront of the sine

[silent sigil]

just multiply the sine approximation by 2 theta

[sick elbow]

okay so

1 - 4 ( 1 - theta^2/2 ) all over 6 theta

?

[silent sigil]

cos(4x)≈1-((4x)^2)/2

[silent sigil]

2x*3x=6x^2

[sick elbow]

whats over 2

all of it?

or just the 4x^2

[silent sigil]

this is a bit clearer

[sick elbow]

okay thanks

[silent sigil]

so for that cosine function, you replace theta with 4 theta

since 4 theta is the input

[sick elbow]

icl im lost

could u write out some working so i can see

idk what im doing wrong

but im just getting to stupid answers

[silent sigil]

ibr im too tired to do that BUT luckily i remember that question from a past paper and was able to find the model answer

[sick elbow]

thanks appreciate it

im so stupid i did everything write i just said 2x*3x = 6x 🤦‍♂️

[sick elbow]

u good to help with one more?

[silent sigil]

let's see it