Find exact value of cot(-165) degrees using difference

[xethissyx]

I need help finding the value of cot(-165) using the difference formulas. Must see all work please. I dont really know how to get started with this problem...

 

[arthur ohlsten]

Cot -165

I find it difficult to work with Cot , so I shall convert to sin and cos
Cot [-165]= Cos[-165]/sin[-165]

cot [-165]=cot[-90-75]
cot -165=cos[-90-75] / sin[-90-75]
cot -165= cos[90+75] /-sin[90+75]

but cos[a+b]=cosacosb-sinasinb
or cos[90+75]=cos90cos75-sin90sin75
cos[90+75]= -sin75

sin[a+b]=sinacosb+sinbcosa
sin[90+75]=sin90 cos75+sin75 cos90
sin[90+75]=cos75

substituting yields
cot[-165]=-sin75/-cos75
cot[-165]=sin75/cos75 answer OR

but sin 75=sin[45+30]
sin 75=sin45cos30+cos45sin30
sin 75=[sqrt3/2sqrt2]+1/(2sqrt2)
sin75=[1+sqrt3]/[2sqrt2]

and cos75=cos[45+30]
cos75=cos45cos30-sin45sin30
cos75=sqrt3/(2sqrt2) - 1/(2sqrt2)
cos45=[sqrt3-1]/[2sqrt2]

substitute
cot[-165]=[sqrt3 +1] / [sqrt3 -1] answer OR

cot[-165]=[sqrt3 +1]/[sqrt3 -1] times [sqrt3+1]/[sqrt3+1]
cot[-165]= [sqrt3+1]^2/[3-1]
cot[-165]=1/2 [sqrt3+1]^2 answer

Arthur

 

[xethissyx]

that gives me an answer of 3.73 but the answer is .066483
I got that answer multiple times. How come the answer is .066483 on the calculator and I continuously dont get it

 

[skeeter]

check that your calculator is in degree mode ... what you "think" is the correct answer is because you calculated in radian mode.

cot(-165) = 1/tan(-165) = 3.732050808...

 

[arthur ohlsten]

Skeeter is correct. The answer given by myself is correct.
Arthur