• We need your support!

    We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
    Click here to Donate Now (View Announcement)

Mathematics: Post your doubts here!

Messages
455
Reaction score
7,676
Points
503
IDK :p no solution with me thats why m confused. :p
its a homework :3
Well, I cant be 100 % sure here, but here's what I did.
Greatest value of cosine is 1. You will get that when 1/2(theta) is 360
greatest value of sin is also 1. You will get that when 1/2(theta) is 90
Therefore plugging in 1 will give you 7 plus 5 plus 12 which is 24
Now 24 is the greatest value that occurs. For the smallest 'positive' however, you need a positive sign will the largest number i.e. 12 and a negative sign with 5 to get the smallest value. Therefore 1-5 12 will give you 14.
For less working you can even use your answer to part i and then determine cos and sin values
I repeat I'm not sure if that's correct. That was my mental calculation
 
Messages
2,206
Reaction score
2,824
Points
273
Well, I cant be 100 % sure here, but here's what I did.
Greatest value of cosine is 1. You will get that when 1/2(theta) is 360
greatest value of sin is also 1. You will get that when 1/2(theta) is 90
Therefore plugging in 1 will give you 7 plus 5 plus 12 which is 24
Now 24 is the greatest value that occurs. For the smallest 'positive' however, you need a positive sign will the largest number i.e. 12 and a negative sign with 5 to get the smallest value. Therefore 1-5 12 will give you 14.
For less working you can even use your answer to part i and then determine cos and sin values
I repeat I'm not sure if that's correct. That was my mental calculation
I asked my friend answer, he also dont know but knows the direct answer, it is 585.2
and value is 20. Thats what he texted me. Not 24. :)
 
Messages
2,206
Reaction score
2,824
Points
273
Well, I cant be 100 % sure here, but here's what I did.
Greatest value of cosine is 1. You will get that when 1/2(theta) is 360
greatest value of sin is also 1. You will get that when 1/2(theta) is 90
Therefore plugging in 1 will give you 7 plus 5 plus 12 which is 24
Now 24 is the greatest value that occurs. For the smallest 'positive' however, you need a positive sign will the largest number i.e. 12 and a negative sign with 5 to get the smallest value. Therefore 1-5 12 will give you 14.
For less working you can even use your answer to part i and then determine cos and sin values
I repeat I'm not sure if that's correct. That was my mental calculation
7+13cos(1/2@ + 67.38).
Maximum value is when cos(1/2@ + 67.38) = 1
so its 7 + 13 = 20. I know this. :)
Hope u got this :)
 
Messages
3,401
Reaction score
9,793
Points
523
I asked my friend answer, he also dont know but knows the direct answer, it is 585.2
and value is 20. Thats what he texted me. Not 24. :)
to get greatest value of the whole expression, u need to have greatest value of "5 cos x - 12 sin x" (assuming x = 1/2 fi)
let y = cos x - 12 sin x

differentiate y,
dy/dx = -5 sin x - 12 cos x = 0 (to find the turning point)
solve...
x = 112.62, 292.62
one is minma, and one is maxima
one will give u max value of y, and one will give least

max y = 13, gives max of that expression 13 + 7 = 20
min y = -13, gives least value 7 - 13 = -6
 
Messages
455
Reaction score
7,676
Points
503
to get greatest value of the whole expression, u need to have greatest value of "5 cos x - 12 sin x" (assuming x = 1/2 fi)
let y = cos x - 12 sin x

differentiate y,
dy/dx = -5 sin x - 12 cos x = 0 (to find the turning point)
solve...
x = 112.62, 292.62
one is minma, and one is maxima
one will give u max value of y, and one will give least

max y = 13, gives max of that expression 13 + 7 = 20
min y = -13, gives least value 7 - 13 = -6
The question says least 'positive'
 
Messages
3,401
Reaction score
9,793
Points
523
The question says least 'positive'
least positive value of "Fi", which gives largest possible value of that expression.
to get greatest value of the whole expression, u need to have greatest value of "5 cos x - 12 sin x" (assuming x = 1/2 fi)
let y = cos x - 12 sin x

differentiate y,
dy/dx = -5 sin x - 12 cos x = 0 (to find the turning point)
solve...
x = 112.62, 292.62
one is minma, and one is maxima
one will give u max value of y, and one will give least

max y = 13, gives max of that expression 13 + 7 = 20
min y = -13, gives least value 7 - 13 = -6
292.62 is smallest positive value of x to give the largest value of that expression,
is i assumed x = 1/2 fi
fi = 2 x
least fi = 2 * least x
least +ve fi = 2 * 292.62 = 585.24

The Sarcastic Retard :) hope u get this
 
Messages
2,206
Reaction score
2,824
Points
273
lol what?

read the Q again, it asks for least value of fi, which gives the greatest value of that expression.
112.6 gives the smallest value of that expression.
least positive value of "Fi", which gives largest possible value of that expression.

292.62 is smallest positive value of x to give the largest value of that expression,
is i assumed x = 1/2 fi
fi = 2 x
least fi = 2 * least x
least +ve fi = 2 * 292.62 = 585.24

The Sarcastic Retard :) hope u get this
You said 292.62 is smallest positive value, but 112.6 is the smallest positive value. No? o_O
Isnt 112 smaller than 292?
 
Messages
3,401
Reaction score
9,793
Points
523
You said 292.62 is smallest positive value, but 112.6 is the smallest positive value. No? o_O
Isnt 112 smaller than 292?
boy boy boy, read the Q again, it asks for "smallest positive value of fi which will give u the largest possible value of that whole expression"
x = 112.6 gives you 'smallest' value of that exp,
it is x = 292.62 for which occurs the max value of the expression.
 
Top