# Math Help - Inverse trig from an exam paper

1. ## Inverse trig from an exam paper

See the image for details. I solved the first two parts and got stuck on the last part.

2. ## Re: Inverse trig from an exam paper

Originally Posted by bbrain
See the image for details. I solved the first two parts and got stuck on the last part.
Please note that long-standing MHF policy prohibits assistance on exam questions.

3. ## Re: Inverse trig from an exam paper

Originally Posted by skeeter
Please note that long-standing MHF policy prohibits assistance on exam questions.
Unless it's a past exam or a practice exam. Is it?

4. ## Re: Inverse trig from an exam paper

Originally Posted by Prove It
Unless it's a past exam or a practice exam. Is it?
Yes, it is. CIE Pre U june 2010

5. ## Re: Inverse trig from an exam paper

Well for the first, you'll need to make use of the following identities:

\displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}

Start by writing \displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}. What do you think you would do from here?

6. ## Re: Inverse trig from an exam paper

Originally Posted by Prove It
Well for the first, you'll need to make use of the following identities:

\displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}

Start by writing \displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}. What do you think you would do from here?
I have already done the first part. It's the last part I am stuck on.

7. ## Re: Inverse trig from an exam paper

Originally Posted by bbrain
I have already done the first part. It's the last part I am stuck on.
Why didn't I know that? I guess my psychic powers must be a little off today...

8. ## Re: Inverse trig from an exam paper

Originally Posted by Prove It
Why didn't I know that? I guess my psychic powers must be a little off today...