# Thread: Where the hell is my mistake

1. ## Where the hell is my mistake

I have to find f'(x) and f'(1) for f(x) = cos(x) - 2tan(x)

f'(x) = -sin(x) - 2sec^2(x)

finding values of x I evaluate sin^(-1)(x), in this case sin^(-1)(1), am I right?

f'(1) = -sin(x) - 2sec^2(x) = -sin(x) - 2(1+ cot^2(1)) = -sin(1) - 2(1+ 1/tan^2(1)) = -1.570796327 - 2(1+1/0.616850275) = .....

I don't get where is my mistake, can someone show me?

Thanks

2. ## Re: Where the hell is my mistake

If $\displaystyle f'(x) = -\sin{(x)} - 2\sec^2{(x)}$, then $\displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)}$, remembering that your angles will be measured in radians. I have no idea why you are suggesting using inverse trigonometric functions.

If you need help evaluating the sec values, rewrite $\displaystyle \sec{(x)} = \frac{1}{\cos{(x)}}$.

3. ## Re: Where the hell is my mistake

Originally Posted by Prove It
If $\displaystyle f'(x) = -\sin{(x)} - 2\sec^2{(x)}$, then $\displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)}$, remembering that your angles will be measured in radians. I have no idea why you are suggesting using inverse trigonometric functions.

If you need help evaluating the sec values, rewrite $\displaystyle \sec{(x)} = \frac{1}{\cos{(x)}}$.
In this case would it be right in this way,

$\displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)} = -\sin{(1)} - 2\frac{1}{\cos{(1)}} = -\sin{(1)} - 0$

which finally gives me $-0.841470984radians = -48.21273601degrees$

or I'm missing something from basic trigonometry? I'm really frustrated...

4. ## Re: Where the hell is my mistake

You are trying to get a numerical value, not an angle. Just plug this into your calculator AS IS. Do NOT use inverse trigonometric functions. I have no idea why you got that 2/cos(1) is 0...

5. ## Re: Where the hell is my mistake

Originally Posted by Prove It
You are trying to get a numerical value, not an angle. Just plug this into your calculator AS IS. Do NOT use inverse trigonometric functions. I have no idea why you got that 2/cos(1) is 0...
that simple $-7.692508626$ , oh my god