# Thread: Am I on the right track?

1. ## Am I on the right track?

I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

$\displaystyle \sin\frac{\pi}{4}=.7104$
$\displaystyle \cos\frac{\pi}{4}=.7038$
$\displaystyle \tan\frac{\pi}{4}=1.009$
$\displaystyle \csc\frac{\pi}{4}=1.408$
$\displaystyle \sec\frac{\pi}{4}=1.421$
$\displaystyle \cot\frac{\pi}{4}=.9908$

I think I got them right, I consulted a table, so I'm just being double sure.

Thank you!

2. Originally Posted by MathBlaster47
I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

$\displaystyle \sin\frac{\pi}{4}=.7104$
$\displaystyle \cos\frac{\pi}{4}=.7038$
$\displaystyle \tan\frac{\pi}{4}=1.009$
$\displaystyle \csc\frac{\pi}{4}=1.408$
$\displaystyle \sec\frac{\pi}{4}=1.421$
$\displaystyle \cot\frac{\pi}{4}=.9908$

I think I got them right, I consulted a table, so I'm just being double sure.

Thank you!

3. ## Sorry I dont think they are...

$\displaystyle \sin\frac{\pi}{4}=.7104$ that is $\displaystyle \frac{\sqrt2}{2}$
$\displaystyle \cos\frac{\pi}{4}=.7038$ sin and cosine of $\displaystyle \frac{\pi}{4}$ are equal
$\displaystyle \tan\frac{\pi}{4}=1.009$ this is exactly 1.000
$\displaystyle \csc\frac{\pi}{4}=1.408$
$\displaystyle \sec\frac{\pi}{4}=1.421$
$\displaystyle \cot\frac{\pi}{4}=.9908$

Hope it helps..

4. Well...I cheated a little, you see I consulted a table for my answers as I hadn't the slightest idea how to get my answers.
How do I work out such a question?

5. Originally Posted by MathBlaster47
Well...I cheated a little, you see I consulted a table for my answers as I hadn't the slightest idea how to get my answers.
How do I work out such a question?
Math Concepts Explained: Special Angles in Trigonometry

6. ah....Thank you!
An explanation I can understand!

7. Originally Posted by MathBlaster47
I have a few questions that I'm pretty sure that I have solved, but need to make sure of:

Find the exact value of the six trigonometric functions of $\displaystyle \frac{\pi}{4}$ radians.(Leave your answer in radical form.)

$\displaystyle \sin\frac{\pi}{4}=.7104$
$\displaystyle \cos\frac{\pi}{4}=.7038$
$\displaystyle \tan\frac{\pi}{4}=1.009$
$\displaystyle \csc\frac{\pi}{4}=1.408$
$\displaystyle \sec\frac{\pi}{4}=1.421$
$\displaystyle \cot\frac{\pi}{4}=.9908$

I think I got them right, I consulted a table, so I'm just being double sure.

Thank you!
So just to make sure you got the last three:

$\displaystyle \csc\frac{\pi}{4}=\frac{1}{sin\frac{\pi}{4}} = \frac{2}{\sqrt2}=\sqrt2$
$\displaystyle \sec\frac{\pi}{4}=\frac{1}{cos\frac{\pi}{4}} = \frac{2}{\sqrt2}=\sqrt2$
$\displaystyle \cot\frac{\pi}{4}=\frac{1}{tan\frac{\pi}{4}}=\frac {1}{1} = 1$