arithmetic series problem or maybe trig? (1 Viewer)

[Aznmichael92]

hello all, i just came across a maths question which i have problems doing.

Question says, Evaluate

cos^2 1 + cos^2 2 + cos^2 3 + ... + cos^2 87 + cos^2 88 + cos^2 89.

My first instinct is to treat it like an arithmetic series.

So i used formula of n[(a1 + an)/2]

= 89(cos^2 1 + cos^2 89)/2
=24.57

I am not sure if its correct but can someone help me? Thank you very much

 

[tommykins]

Is that in degrees or radians

 

[shaon0]

Is that in degrees or radians

i think degrees. they don't learn radians until they do trig functions.

 

[Aznmichael92]

i think its degrees, havent learnt radians hahaha

 

[tommykins]

using cos@ = sin(90-@)

you have -
cos^2 1 + cos^2 2 + cos^2 3 + ... + cos^2 87 + cos^2 88 + cos^2 89.
= cos^2 1 + cos^2 2 + cos^2 3 + ... + sin^2 3 + sin^2 2 + sin^2 1
since sin^2 @ + cos^2@ = 1
you have 44 of them as it only goes up to 45.

44 + cos^2 45 = 44+1/2 = 44.5

 

[Timothy.Siu]

nice work lol

 

[Aznmichael92]

using cos@ = sin(90-@)

you have -
cos^2 1 + cos^2 2 + cos^2 3 + ... + cos^2 87 + cos^2 88 + cos^2 89.
= cos^2 1 + cos^2 2 + cos^2 3 + ... + sin^2 3 + sin^2 2 + sin^2 1
since sin^2 @ + cos^2@ = 1
you have 44 of them as it only goes up to 45.

44 + cos^2 45 = 44+1/2 = 44.5

ty so it had nothing to do with arithmetic series?

but i tried it, it doesnt seem to work as in, sin^2 1 does not equal to cos^2 89

 

[Timothy.Siu]

ty so it had nothing to do with arithmetic series?

seems not

 

[tommykins]

ty so it had nothing to do with arithmetic series?

but i tried it, it doesnt seem to work as in, sin^2 1 does not equal to cos^2 89

Yes it does.

 

[Aznmichael92]

Yes it does.

it does?

when i input it into calculator doesnt seem to work.

cos^2 1 = 0.2919
sin^2 89 = 0.7397

 

[tommykins]

[cos (1)]^2

 

[Aznmichael92]

[cos (1)]^2

yea i put that in calculator but doenst work either or maybe i am not meant to use calculator?

 

[tommykins]

your calculator is on radians.

 

[Timothy.Siu]

it does?

when i input it into calculator doesnt seem to work.

cos^2 1 = 0.2919
sin^2 89 = 0.7397

thats in radians

 

[Aznmichael92]

oh no how i fix it?

EDIT

nvm i found out thank you so much guys. I LOVE YOUS lol

 

[Timothy.Siu]

well u can click mode until u see a screen with deg rad gra, click the number corresponding to deg (degrees)

 

[Aznmichael92]

well u can click mode until u see a screen with deg rad gra, click the number corresponding to deg (degrees)

TY

 

[SeftonIsAHole]

hmm if you havent learn radiasn let why is your calculator set in rads? haha
Yeah, watch out for that, one of my friends got fuked over in year 9 cause his little sister changed his calculator settings to rads before math exam ;p, but luckily the teachers picked it up and didn't penalise him that badly.

 

[Aznmichael92]

hmm if you havent learn radiasn let why is your calculator set in rads? haha
Yeah, watch out for that, one of my friends got fuked over in year 9 cause his little sister changed his calculator settings to rads before math exam ;p, but luckily the teachers picked it up and didn't penalise him that badly.

um i dont know why its on radian, i think my cousins were playing around with it the other day and put it on radian