# Small problem in 9709_w07_qp_3

#### Zazzyo

See in ques 7 on page 3...

Code:
http://www.xtremepapers.net/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w07_qp_3.pdf

how do we decide whether we keep the calculator in radian mode or degree mode?

#### Zazzyo

and i am unable to do part (iii) of this question 7 aswell.. can someone shed some light onit aswell?

#### anamsohail

i hope this helps in understanding why we use radians....
other than circles....we use it when we arent dealing with any dimensions...thats what i understood from this link...
and in this question 7...population of insects is to be calculated..which is dimensionless...so maybe thats why we have to solve in radians..!!

#### anamsohail

For part iii) here's the solution...

rearrange the equation obtained in part i) ln N = 50ksin(0.02t) + ln 125

bring all the terms with "ln" on one side... ln N - ln 125 = 50ksin(0.02t)
apply log rules...this will become...ln (N/125)=50ksin(0.02t)
convert it into index form....

N/125 = e^(50ksin(0.02t))

put the value of k calculated in part ii) and you'll get.... N/125 = e^(0.5sin90.02t))
shift 125 to the other side so as to make N the subject and obtain final answer...

N = 125e^(0.5sin90.02t))

for the least value...put the term with "sin" equal to -1...as it is its least value..
and solve...
N = 125e^(0.5 x (-1))
N = 75.8
thts the least value of N!

#### Zazzyo

thanx guys.. still not clear with the radians concept though... so is it like.. if its not mentioned to do in degrees we do it in radians?

#### anamsohail

not really...generally we do it in degrees, if nothing specific is mentioned..
in this particular question no dimensions were taken into account...and a population cant be measured in degrees...so it had to be in radians...just read the question carefully and then decide which one to use...radians or degrees....!