Find a possible solution to the equation sin (3x+13)=cos(4x)

- ASAPT

Find a possible solution to the equation sin (3x+13)=cos(4x)

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- ASAPT

@LegendarySadist

- ASAPT

its part of my geometry course @LegendarySadist trig is one of the sections lol

- ASAPT

@misssunshinexxoxo @ybarrap

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## More answers

- ASAPT

nah at my schools it goes algebra 1 geometry algebra 3 and pre calc or discrete math im in geometry summer school

- ASAPT

*algebra 2

- freckles

use a co-function identity

- freckles

for example, recall one of the co-function identities is:
\[\cos(u)=\sin(\frac{\pi}{2}-u)\]

- ASAPT

wow that really confused me

- freckles

why does it confuse you?

- ASAPT

because this stuff is like another language to me

- freckles

but why does the identity confuse you?

- freckles

is it because you never seen it?

- ASAPT

kinda this is my first time learning this

- freckles

|dw:1436410191044:dw|

- freckles

could you find cos(theta)
and sin(90-theta) using this right triangle ?

- freckles

|dw:1436410266489:dw|

- freckles

\[\sin(90-\theta)=\frac{v}{c} \text{ and } \cos(\theta)=\frac{v}{c} \\ \text{ that means } \sin(90-\theta)=\cos(\theta) \\ \]
of course this is all true if we are working in degress

- freckles

since I used 90 deg there

- freckles

but we can do the same thing for radians
and say
\[\sin(\frac{\pi}{2}-\theta)=\cos(\theta)\]

- ASAPT

would the answer be 13?

- freckles

\[\sin(3x+13)=\cos(4x) \\ \text{ by cofunction identity you have that you can find a solution from } \\ \text{ setting the insides of this thingy equal } \\ \sin(3x+13)=\sin(\frac{\pi}{2}-4x)\]

- ASAPT

so what would that make the answer be?

- freckles

set the insides equal

- freckles

and solve for x

- freckles

\[3x+13=\frac{\pi}{2}-4x \]

- ASAPT

I still don't get my answer

- freckles

to solve a linear equation
first you do:
you put all your x terms on one side and your non-x terms on the opposing side
by adding and subtracting stuff on both sides

- ASAPT

oh so its 11

- freckles

your answer should have pi in it somewhere so 11 isn't the answer

- freckles

or a answer in this case

- freckles

In general to solve the linear equations of the form ax+b=cx+d
you do:
\[ax+b=cx+d \\ \text{ subtract} cx \text{ on both sides } ax-cx+b=cx-cx+d \\ \text{ now } ax-cx=(a-c)x \text{ and } cx-cx=0 \\ \text{ so we have } (a-c)x+b=0+d \\ \text{ now subtract } b \text{ on both sides } (a-c)x+b-b=d-b \\ (a-c)x+0=d-b \\ (a-c)x=d-b \\ \text{ now final step is to divide }(a-c) \text{ on both sides } \\ \text{ so we have } x=\frac{d-b}{a-c}\]

- ASAPT

the options are 11 -13 13 and 0

- freckles

oh then you didn't have to find a possible solution using any identities
just plug in those numbers to see which gives you the same thing on both sides

- ASAPT

so what would the answer come out to be

- freckles

have you tried pluggin in the choices as I suggested above?

- ASAPT

i only have 1 minute until i have to submit it

- freckles

I think they mean all of that to be in degrees
so put your calculator on degrees
and see which of the following is true:
\[\sin(3(0^o)+13^o)=\cos(4(0^o) ) \\ \sin(3(11^o)+13^o)=\cos(4(11^o)) \\ \sin(3(13^o)+13^o)=\cos(4(13^o)) \\ \sin(3(-13^o)+13^o)=\cos(4(-13^o))\]

- freckles

you can definitely rule out the first since we know sin(13 deg) isn't cos(0 deg)
then check the second equation with 11 degs
and so on... until you have the same thing on both sides

- freckles

what is sin(3*11 deg+13 deg)=?

- freckles

give you a hint 3*11+13=33+13=46
and guess what 90-46 is?

- freckles

recall the above
you can do this part without calculator
come on
you know sin(x)=cos(90-x)
so sin(46)=cos( ? )

- freckles

also it would be helpful in the future if you say if we are working in deg or radians
because I thought it was radians until I seen your choices

- freckles

good luck

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