Solving the Equation

[m7r23]

I have no idea where to start out at, I just need someone to start me out.

solve the equations for t, 0 _< t _< 2pie
sin(2t)=2cost

and simplify hte expression sin)2cos-1x) in terms of x without trigonometric function.

 

[tkhunny]

Start with sin(2t) = 2sin(t)cos(t). Do NOT divide by cos(t) after that!

Can't understand the second one.

 

[m7r23]

ok thats it for the first one. I guess I'm really lost. I need to read this book for the 4th time. and the second one should be


Simplify the expression sin(2cos-1x) in terms of x without trigonometric functions.

 

[tkhunny]

You didn't share your results.

On the second,

1) Draw a right traingle.
2) Label one of the acute angles A
3) Label the Hypotenuse 1 (one)
4) Label the side opposite A, x
5) Notice how cos(A) = x/1 = x, so that cos^-1(x) = A
6) Again with the identity, sin(2A) = 2sin(A)cos(A)
7) A couple more steps to go. Can you finish?

 

[skeeter]

sin(2t) = 2cost

2sintcost = 2cost

2sintcost - 2cost = 0

2cost(sint - 1) = 0

now ... set each factor equal to 0 and solve for values of t within the given domain.



btw ... the expression sin(2cos-1x) doesn't make any sense.

do you mean sin(2cos^-1x) ???

 

[m7r23]

yeah i meant -1 exponent for the second one. And ok, i got the first one after reading ya'll two posts and the book again.

 

[pka]

\(\displaystyle \L
\begin{array}{l}
A = \arccos (x) \\
\cos (A) = x \\
\sin (A) = \sqrt {1 - x^2 } \\
\sin (\arccos (x)) = \sqrt {1 - x^2 } \\
\end{array}\)

 

[m7r23]

\(\displaystyle \L
\begin{array}{l}
A = \arccos (x) \\
\cos (A) = x \\
\sin (A) = \sqrt {1 - x^2 } \\
\sin (\arccos (x)) = \sqrt {1 - x^2 } \\
\end{array}\)

please tell me that not the answer to the second problem, if it is. I'm in a lot of trouble. Trignometry is just not my subject at all. May I ask how did you arrive to this solution?

 

[pka]

NO! But this is the answer
\(\displaystyle \L
\begin{array}{l}
\sin (2A) & = & 2\sin (A)\cos (A) \\
& = & 2\left( {\sqrt {1 - x^2 } } \right)(x) \\
& = & 2x\sqrt {1 - x^2 } \\
\end{array}\)

 

[m7r23]

Ok, thanks for the help. I will try my best. I will have to find similar examples on the internet so i can practice, because these are kicking my butt.

 

[tkhunny]

Did you do the first six steps I gave you?

If so, that didn't lead you anywhere?