1. ## Evaluate without calculator

Help please. Sorry if Im posting several threads. I have an examination tomorrow and need to know how to solve this.

1. $\displaystyle cot [{Arcsec (-2 \sqrt{3/4}) }]$

2. $\displaystyle sin [{arctan (\frac{-5}{12}) }]$

3. $\displaystyle Cos^{-1}[{1/2\sqrt{2} cos[Sin^{-1} (-1) }]$

2. Originally Posted by reiward
Help please. Sorry if Im posting several threads. I have an examination tomorrow and need to know how to solve this.

1. $\displaystyle cot [{Arcsec (-2 \sqrt{3/4}) }]$

2. $\displaystyle sin [{arctan (\frac{-5}{12}) }]$

3. $\displaystyle Cos^{-1}[{1/2\sqrt{2} cos[Sin^{-1} (-1) }]$
I will do 1. The others follow a similar approach.

Let $\displaystyle \text{arcsec} (- \sqrt{3}) = \alpha \Rightarrow \sec \alpha = - \sqrt{3}$ (think carefully about what quadrant $\displaystyle \alpha$ is in).

Knowing $\displaystyle \sec \alpha = - \sqrt{3}$ you should be able to calculate $\displaystyle \cot \alpha$.

3. Originally Posted by mr fantastic
I will do 1. The others follow a similar approach.

Let $\displaystyle \text{arcsec} (- \sqrt{3}) = \alpha \Rightarrow \sec \alpha = - \sqrt{3}$ (think carefully about what quadrant $\displaystyle \alpha$ is in).

Knowing $\displaystyle \sec \alpha = - \sqrt{3}$ you should be able to calculate $\displaystyle \cot \alpha$.
Oh okay. So I need to draw the graph.

Uhm. Can you help me on the last number? I'm clueless

4. Originally Posted by reiward
Oh okay. So I need to draw the graph.

Uhm. Can you help me on the last number? I'm clueless
Perhaps start with the fact that $\displaystyle \sin^{-1} (-1) = - \frac{\pi}{2}$ ....