I honestly don’t know the first step to doing any of this on the worksheet and I can’t find any resources to these specific questions, does anyone know how to solve these?
#Pre-calc: equivalent representations
frank goblet
spiral blazeBOT
rose void
I honestly don’t know the first step to doing any of this on the worksheet and I...
The first one you can use 2sin(x)cos(x) = sin(2x)
frank goblet
Where does that come from, is it just a rule?
rose void
The second one is cos²(x) - sin²(x) = cos(2x)
rose void
Where does that come from, is it just a rule?
Those are identities
You said you couldnt find resources or some
Are you allowed to use trigonometric table?
frank goblet
Those are identities
So what are all the trig identities
frank goblet
Are you allowed to use trigonometric table?
I think so
rose void
There are plenty, but you need those two
rose void
I think so
If so then 5π/4 and 7π/6 should be on the table
rose void
well then
if you still don't know the values tho you can make use of sine and cosine addition theorem
upper peakBOT
adonhs
rose void
For example 5π/4 = 4π/4 + π/4 = π + π/4
π and π/4 are very easy angles to memorize.
upper peakBOT
adonhs
rose void
The other two identities I just provided above as well.
rose void
I don't know a specific name for that
You can prove it though using sine addition theorem
You may try it out yourself first 😄
||sin(2x) = sin(x+x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)||
frank goblet
Would the exact value be -√2/2?
rose void
Would the exact value be -√2/2?
👏🏻
rose void
it's good
frank goblet
I think 1 and 2 makes more sense, what about the verify questions how would u do those
rose void
You mean proving the identities?
rose void
Try to make use of what I provided
2sin(x)cos(x) = sin(2x)
cos²(x) - sin²(x) = cos(2x)
cot(x) = cos(x)/sin(x)
frank goblet
I’m not sure maybe we’re doing different processes to solve😭 cause our teacher taught us to change the trig identities. Like for 3 we would change the equation on the right of the equal sign to look like the one on the left
rose void
I’m not sure maybe we’re doing different processes to solve😭 cause our teacher ...
yea
that's how you approach it
rose void
2sin(x)cos(x) = sin(2x)
cos²(x) - sin²(x) = cos(2x)
cot(x) = cos(x)/sin(x)
Those trig identities might just help you
frank goblet
Ok I think I did it right
rose void
show
rose void
That look right?🤔
👏🏻
You made use of 1 + cot² = csc²
and also
csc = 1/sin
But question did you use the internet, or did your teacher tell you some identites by themself?
frank goblet
A little bit of both honestly
rose void
that's good
frank goblet
I know the csc = 1/sin stuff already, but had to search up the 1 + cot part
rose void
you're doing great so far
there are people who are very clueless
but you know what you are doing, you just need the right puzzles to begin with
frank goblet
I’d say I’m close to clueless but yeah!
rose void
you are rather indecisive😎
frank goblet
Pfffft I guess
How would I do 4, I’m not sure since it’s 1 - sin(2x) instead of the trig identities that I went off of in the previous question which was just sin(2x)
rose void
honestly i would try (a-b)² = a² - 2ab + b²
😄
I am sure you know
1 = sin² + cos²
that should work 😄
rose void
👏🏻 🔥