Find the value of $ arctan(sin(frac{3pi}{4})) $

To find the value of $ \arctan(\sin(\frac{3\pi}{4})) $, we first need to find the value of $ \sin(\frac{3\pi}{4}) $.

$ \sin(\frac{3\pi}{4}) = \sin(\pi – \frac{\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $

Now, we need to determine the value of $ \arctan(\frac{\sqrt{2}}{2}) $.

Since $ \arctan(x) $ is the inverse of $ \tan(x) $, we seek an angle $ \theta $ such that:

$ \tan(\theta) = \frac{\sqrt{2}}{2} $

One such angle is $ \theta = \frac{\pi}{4} $, but considering the range of $ \arctan $, the solution is:

$ \arctan(\sin(\frac{3\pi}{4})) = \arctan(\frac{\sqrt{2}}{2}) = \frac{\pi}{4} $

To find the value of $ arctan(sin(frac{3pi}{4})) $, we start by finding the value of $ sin(frac{3pi}{4}) $.

$ sin(frac{3pi}{4}) = sin(pi – frac{pi}{4}) = sin(frac{pi}{4}) = frac{sqrt{2}}{2} $

Next, we determine the value of $ arctan(frac{sqrt{2}}{2}) $.

The angle corresponding to $ an( heta) = frac{sqrt{2}}{2} $ is $ heta = frac{pi}{4} $.

Therefore:

$ arctan(sin(frac{3pi}{4})) = arctan(frac{sqrt{2}}{2}) = frac{pi}{4} $

To find the value of $ arctan(sin(frac{3pi}{4})) $, we first calculate $ sin(frac{3pi}{4}) $:

$ sin(frac{3pi}{4}) = frac{sqrt{2}}{2} $

Then, find $ arctan(frac{sqrt{2}}{2}) $:

$ arctan(frac{sqrt{2}}{2}) = frac{pi}{4} $

Start Using PopAi Today