1. ## 2 questions

Hi i'm stuck on 2 questions and wondering if you can help me out.

1 ) The area of a sector of a circle with radius r cm is fixed at 16 square centimetres, show that the perimeter P cm of the sector OPQ is given by
P = 2 (r + 16/r).

2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360

in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.

thanks for any help

2. ## Ok

Originally Posted by Maths409
Hi i'm stuck on 2 questions and wondering if you can help me out.

1 ) The area of a sector of a circle with radius r cm is fixed at 16 square centimetres, show that the perimeter P cm of the sector OPQ is given by
P = 2 (r + 16/r).

2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360

in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.

thanks for any help
Ok I will give you a hint the area of a sector is $\displaystyle A=\frac{1}{2}r^2\theta$

3. any posibility of you showing me a few lines of what to do?

my brain is completely dead and this needs to be finished asap

4. Originally Posted by Mathstud28
Ok I will give you a hint the area of a sector is $\displaystyle A=\frac{1}{2}r^2\theta$
1. Use the above formula to get $\displaystyle \theta$ in terms of r.

2. Arc length $\displaystyle = \theta r$.

5. Originally Posted by Maths409
[snip]
2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360

in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.

thanks for any help
Use the compound angle formula to expand $\displaystyle k \cos (x - a)$.

Now equate the coefficient of cos x with 1 and the coefficient of sin x with 2 to get two equations that you solve simultaneously for a and k.