Question

Help Please - Trig!

Determine the exact value for:

Answer 1

\[(Sin \left(\begin{matrix}3\pi \\ 4\end{matrix}\right) - \cos \left(\begin{matrix}5\pi \\ 3\end{matrix}\right))^{2}\]

Answer 2

You have to know the exact values of sin(3pi/4) and cos(5pi/3).
Both can be found with the unit circle.
So first draw a unit circle and find the point on it that corresponds with 3pi/4.

Answer 3

(1/sq2 - 1/2)^2

Answer 4

Im having problems getting the final answer, it looks close but its not the same, i understnad how to do it but can you show me the steps so i see where i went wrong? I think it might be an expanding error but I can't find it

Answer 5

\[(1/\text{sq2}-1/2){}^{\wedge}2=\frac{1}{4} \left(3-2 \sqrt{2}\right) \]

Answer 6

I think you know sin(3pi/4) is \[\frac{ 1 }{ 2}\sqrt{2} \]
Also, cos(5pi/3)=1/2.
The only thing to do now, is to caalculate the square of the difference

Answer 7

hmm, when I expanded I got: \[\frac{ 1 }{ 4 } + \frac{ 1 }{2 \sqrt{2} } + \frac{ 1 }{2 \sqrt{2} } + \frac{ 1 }{ 4 }\]

Answer 8

ahh, i see where i went wrong, the 1/4 is supposed to be 1/2

Answer 9

correct?

Answer 10

This is:\[\left( \frac{ 1 }{ 2 }\sqrt{2}-\frac{ 1 }{ 2 } \right)^2\]So if you expand, you get:\[\left( \frac{ 1 }{ 2 }\sqrt{2} \right)^2-2 \cdot \frac{ 1 }{ 2 }\sqrt{2}\cdot \frac{ 1 }{ 2 }+\left( \frac{ 1 }{ 2 } \right)^2=\]\[\frac{ 1 }{ 2 }-\frac{ 1 }{ 2 }\sqrt{2}+\frac{ 1 }{ 4 }=\frac{ 3 }{ 4 }-\frac{ 1 }{ 2 }\sqrt{2}\]

Answer 11

Now if you factor out 1/4, you get:\[\frac{ 1 }{ 4 }\left( 3-2\sqrt{2} \right)\]

Answer 12

shouldnt the sq2 be on the bottom of 1/2 ? so like 1/2sq2?

Answer 13

And, yess, that first 1/4 should be 1/2, because:\[\left( \frac{ 1 }{ 2 }\sqrt{2} \right)^2=\frac{ 1 }{ 4 }\cdot 2=\frac{ 1 }{ 2 }\]

Answer 14

Both are the same:\[\frac{ 1 }{ \sqrt{2} }=\frac{ 1 }{ \sqrt{2} }\cdot \frac{ \sqrt{2} }{ \sqrt{2} }=\frac{ \sqrt{2} }{ 2 }=\frac{ 1 }{ 2}\sqrt{2}\]

Answer 15

ahh alright, i think the 1/4 in the beggining mest me up, thanks for your help!

Answer 16

YW!