Homework Help: Trigonometry help.

1. Feb 7, 2010

ibysaiyan

1.
Hi
Its the bit (c) where i am stuck at although it doesn't look much complicated, for all i know is that max value for cos =1 , so cos inverse becomes 0. The answer on the mark scheme is theta = 326 which i cant figure out.Thanks
2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 7, 2010

kg4pae

I'm just wondering, have you tried it? I would start by observing that

$$cos(\theta + \alpha) = cos(\theta) cos(\alpha) - sin(\theta) sin(\alpha)$$

After solving for $$\alpha$$, you then can find a maximum $$cos(\theta+\alpha)$$ which when multiplied by R will give the answer to part (c).

If you need further help, post your work so far.

3. Feb 7, 2010

ibysaiyan

Ah how weird i just did another similar question of which i got the answers hmm anyway, here is what i did:
i got the R value square root. 13 (by equating co-efficients of sin and cos),
theta 33.7.
P.S: Sorry i have yet to become latex friendly , if only someone could post me a tutorial on how to use it lol .

4. Feb 7, 2010

kg4pae

Note that $$cos(\theta+\alpha)=1$$ means that $$\theta=-\alpha$$. However, the pattern repeats every $$360^o$$.

5. Feb 7, 2010

ibysaiyan

Oh! would i let R$$cos(\theta+\alpha)$$= 1?

6. Feb 7, 2010

kg4pae

No problem. A good start with LaTex is http://frodo.elon.edu/tutorial/tutorial/". Others can be found by Googling "latex tutorial". At any rate, take care, 73s and clear skies.

Last edited by a moderator: Apr 24, 2017
7. Feb 7, 2010

ibysaiyan

Thanks alot!:) for the link .

Last edited by a moderator: Apr 24, 2017
8. Feb 7, 2010

kg4pae

Not quite. Let $$cos(\theta+\alpha)=1$$. That will give the maximum for $$3 cos(\theta) - 2 sin(\theta)$$ after it is multiplied by R. Since R is effectively a constant any maximum of $$cos(\theta+\alpha)$$ will be proportionate to $$R cos(\theta+\alpha)=3 cos(\theta) - 2 sin(\theta)$$.