a level trig | Revision Server | Page 1

tender sedge Mar 3, 2024, 1:23 PM

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how would u do this using graph method (not cast diagram)

blazing solstice Mar 3, 2024, 1:23 PM

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first change it to sine

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so sin(x + π/15) = -1/√2

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then sine inverse both sides

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x + π/15 = -π/4 (using calcultor)

tender sedge Mar 3, 2024, 1:24 PM

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yeah i got there

blazing solstice Mar 3, 2024, 1:25 PM

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then ibr just use the formulae, graph and cast are stupid

tender sedge Mar 3, 2024, 1:25 PM

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what formula?

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i can only do these type of q's with graph method

blazing solstice Mar 3, 2024, 1:25 PM

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sin(x) = sin(π-x), so u always do π-x to get the next solution

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so id do π - (-π/4), which gets 5π/4

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so i have -π/4 and 5π/4 and for all other solutions i just need to add or subtract 2π from both of them

tender sedge Mar 3, 2024, 1:26 PM

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ngl idk whats going on

blazing solstice Mar 3, 2024, 1:26 PM

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so

tender sedge Mar 3, 2024, 1:26 PM

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where did u pull sin(x) = sin(pi-x)

blazing solstice Mar 3, 2024, 1:26 PM

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i got -π/4 from my calculator

tender sedge Mar 3, 2024, 1:26 PM

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is that just a general formula

blazing solstice Mar 3, 2024, 1:26 PM

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tender sedge where did u pull sin(x) = sin(pi-x)

thats just a general sine formula

tender sedge Mar 3, 2024, 1:27 PM

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whats the general one for cos and tan

blazing solstice Mar 3, 2024, 1:27 PM

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for cosine its cos(x) = cos(2π-x)

tender sedge Mar 3, 2024, 1:27 PM

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how did u derive those

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or is it not worth learning

blazing solstice Mar 3, 2024, 1:27 PM

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and then for tan u can just freely add or subtract pi

blazing solstice Mar 3, 2024, 1:27 PM

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tender sedge or is it not worth learning

not worth learning icl its jus from the graph

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i mean if youve learnt the addition formulae u could proce it

tender sedge Mar 3, 2024, 1:27 PM

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ight lemme write those formulas down

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i have

blazing solstice Mar 3, 2024, 1:28 PM

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so sin(π-x) = sin(π)cos(x) - cos(π)sin(x) = sin(x)

tender sedge Mar 3, 2024, 1:29 PM

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damn alr

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got that all down

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i'll learn that

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going back tho

blazing solstice Mar 3, 2024, 1:29 PM

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so going back

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u get -π/4 on ur calculator

tender sedge Mar 3, 2024, 1:29 PM

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yeah i got that

blazing solstice Mar 3, 2024, 1:29 PM

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then for sine u always do π-ans

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so u get 5π/4

tender sedge Mar 3, 2024, 1:29 PM

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u just spam that until u hit the interval?

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of 2pi

blazing solstice Mar 3, 2024, 1:30 PM

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those r ur 2 standard solutions for all other solutions u jus add or subtract 2π

blazing solstice Mar 3, 2024, 1:30 PM

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tender sedge u just spam that until u hit the interval?

nah if u π-ans again u go back to -π/4

tender sedge Mar 3, 2024, 1:30 PM

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i just realised that

blazing solstice Mar 3, 2024, 1:30 PM

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blazing solstice those r ur 2 standard solutions for all other solutions u jus add or subtract 2π

so 5π/4 + 2π = 13π/4 would also be a solution but its not in range

surreal dock Mar 3, 2024, 1:30 PM

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You can also add 2pi but most times that makes it outside the range

tender sedge Mar 3, 2024, 1:31 PM

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blazing solstice those r ur 2 standard solutions for all other solutions u jus add or subtract 2π

is this the case for every single one

blazing solstice Mar 3, 2024, 1:31 PM

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but -π/4 + 2π = 7π/4 would be a solution that is in range

tender sedge Mar 3, 2024, 1:31 PM

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like for cos and tan

blazing solstice Mar 3, 2024, 1:31 PM

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tender sedge is this the case for every single one

whenever its sine yh

tender sedge Mar 3, 2024, 1:31 PM

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ah

blazing solstice Mar 3, 2024, 1:31 PM

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tender sedge like for cos and tan

well for cos yeah, but u gotta do 2π- ans

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and then for tan u jus add/subtract π

tender sedge Mar 3, 2024, 1:32 PM

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blazing solstice so 5π/4 + 2π = 13π/4 would also be a solution but its not in range

so

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once u get ur two standard solutions

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u just add or subtract 2pi?

blazing solstice Mar 3, 2024, 1:32 PM

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yh

tender sedge Mar 3, 2024, 1:32 PM

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to both ur standard solutions

blazing solstice Mar 3, 2024, 1:32 PM

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until u got all possible ones in range

tender sedge Mar 3, 2024, 1:32 PM

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to see if it's in the given interval?

blazing solstice Mar 3, 2024, 1:32 PM

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tender sedge u just add or subtract 2pi?

and u can continue doing that forever until its in range

tender sedge Mar 3, 2024, 1:32 PM

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fuck man how did i not know about those formulas

blazing solstice Mar 3, 2024, 1:33 PM

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helps me a lot

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cast and graphs r jus long for no reason

tender sedge Mar 3, 2024, 1:33 PM

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i just suffer with the graph

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because i'm not learning cast

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that is just aids

blazing solstice Mar 3, 2024, 1:33 PM

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😭

tender sedge Mar 3, 2024, 1:33 PM

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alr lemme try this

blazing solstice Mar 3, 2024, 1:33 PM

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u in y13, or u doing fm?

tender sedge Mar 3, 2024, 1:35 PM

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oh wtf i just realised ur in year 12

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im y13

blazing solstice Mar 3, 2024, 1:35 PM

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calm

tender sedge Mar 3, 2024, 1:35 PM

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i just skipped this chapter cuz its long

blazing solstice Mar 3, 2024, 1:35 PM

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tender sedge oh wtf i just realised ur in year 12

im doing fm so we do all of normal maths in y12

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but we dont take the exam

tender sedge Mar 3, 2024, 1:36 PM

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long

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but nice tho

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idk why my school didnt teach us the formula u js told me

blazing solstice Mar 3, 2024, 1:36 PM

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tender sedge idk why my school didnt teach us the formula u js told me

a bit of a sheg

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practice a lot w it so u get used to it

tender sedge Mar 3, 2024, 1:37 PM

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i should

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but

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i don't know a mark scheme that uses this

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solution bank just does CAST

blazing solstice Mar 3, 2024, 1:37 PM

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the markscheme only gives u marks for the solutions tho

tender sedge Mar 3, 2024, 1:37 PM

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i just meant

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if i'm wrong

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i would wanna c how someone would use the formula

blazing solstice Mar 3, 2024, 1:38 PM

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oh i see

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i mean its the same thing everytime

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like it doesnt rlly change

tender sedge Mar 3, 2024, 1:38 PM

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that's true

blazing solstice Mar 3, 2024, 1:38 PM

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ive never seen it change

tender sedge Mar 3, 2024, 1:38 PM

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should i do madasmaths

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or js mixed exercise

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to practice those formulas

blazing solstice Mar 3, 2024, 1:38 PM

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me personally i think mixed exercise

tender sedge Mar 3, 2024, 1:38 PM

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fairs

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ill just do all the q's there

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dont think that's enough practice tho ibr

blazing solstice Mar 3, 2024, 1:39 PM

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theres a lot tho

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if u consistently get them right then ur good

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bc like if u get them right everytime in the mixed exercise, why would u get it wrong in the exam

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theres no difference

tender sedge Mar 3, 2024, 1:41 PM

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mm

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true

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@blazing solstice for the q

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i got x = 11/6π and x = π/6

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can u show me how u would get the other 2 cuz mine keeps going out of range

blazing solstice Mar 3, 2024, 1:48 PM

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so id do cos^2x = 3/4

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square root both sides

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cosx = √3/2 or -√3/2

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focusing on cos(x) = √3/2

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id cos inverse both sides to get x = π/6

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then i do 2π-π/6 = 11π/6

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whats the range?

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@tender sedge

tender sedge Mar 3, 2024, 1:49 PM

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blazing solstice Mar 3, 2024, 1:50 PM

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blazing solstice cosx = √3/2 or -√3/2

u prolly forgot that cos(x) could also be -√3/2

tender sedge Mar 3, 2024, 1:50 PM

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ohhhh

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yeah mb

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bro this formula is sick wtf

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appreciate it

#a level trig