Solving Sin(2α)=-8/17 Using Identities

[VietDao29]

no, i know the unit circle. I spent a long time trying to figure out how they got all the sins and cos. I had to draw a 45 45 triangle with a hypotenous of 1 and then go from there to find the rest using pythagerian theory and what not. i have solved right triangles many times using the Pythagorean therom. I know its not random but sure seems like it. i googled trig identities and the sin²(2a)=cos²(2a) is not listed in my book or on goolge, so that's why it seems random. how should have i known that i could do that when all the examples in the book don't even list that as a possibility. So it seemed random because its like someone just grabbed the sin and cos functions and put them in there and set it = to 1.

thats why i asked if sin^3+cos^3=1 would work because to me that's what happened earlier, random sins and cos's were put into the pythagerian theory. haha. but sin^3+cos^3=1 does indeed work. i just did sin(90)^3+cos(90)^3 and it =1

so now I am lost again. haha.oh well. ill figure it out

An identity is an equality that holds true for every value of the variable(s) in that equality.

Example of an identity: sin²x + cos²x = 1. This equality holds true regardless of what value x takes. Try plugging in some random values for x to see.

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However, sin³x + cos³x = 1 is indeed, NOT an identity. The above equality may hold for some specific value of x, but it will fail in other cases.

sin³x + cos³x = 1 will hold true for x = 90^o, or even when x = 0^o.

But it will FAIL to hold true, when x = 45^o, and many many other values.

Regards,

 

[HallsofIvy]

but sin^3+cos^3=1 does indeed work. i just did sin(90)^3+cos(90)^3 and it =1

I'm beginning to think this whole thread is a troll. If thiws goes on much longer I will close or delete this thread.

 

[LT72884]

I'm beginning to think this whole thread is a troll. If thiws goes on much longer I will close or delete this thread.

Ok sorry for a late reply. i don't start work till evening time and i don't have a pc at home for the time being.

Im beginning to understand some things about identities. i tried some random values for x and saw the results. With the cubed one i THOUGHT would work, i realized last night around 4 am that it only worked because 1 cubed is 1 and 0 cubed is, well, 0. didnt realize that till later though. I am beginning to wonder that the sqaures have something to do with it and it can only be squares and not cubes. SO what is so important about squares?

Oh and what is a troll thread? is that where someone is paid to just make random non sense on a thread?

Im sorry if it seems like that but its not. I have never done trig so for me to always remember that the sin of 90 = 1 or whatever it is is new to me. i still don't have the cos and sin memorized for all unit circle yet. haha. i have no time because homework is so demanding. haha

i was under the impression that the pythagerian theory had to stay in the form of sin²a and nothing else, hence why it seemed so random to me what you guys did. BUT I am trying to see what is going on here. Please forgive. I really really appreciate the help and time you guys have shown me. I have been a member here for a year or so and have posted other questions regarding force and mass of a 747. haha

anyway, i would like to understand why the idenitity actually works. Is it because of the squares or the fact that it uses co functions? or is it both?

Thanks

Matt

thanks