Question

Evaluate cot 45° without using a calculator by using ratios in a reference triangle.

Answer 1

im totally lost

Answer 2

@phi can u plz help, thanks

Answer 3

do any of u know how to solve?

Answer 4

you need to take tHe referene triangle: THe Cot of 45 is te same as 1/tan(45) wiCH is tHe Hypotenuse/adjaent or \[\cot (45)=\frac{ 1 }{ \tan (45) }=\frac{ Hyp }{ adj }=\frac{ \sqrt{2} }{ 1 }=\sqrt{2}\]

Answer 5

@ivancsc1996 it should be cot = adj/opp, since tan is opp/adj.

Answer 6

OH you are rigHt

Answer 7

cot = x/y = cos/sin? right?

Answer 8

tHen tHe answer is 1

Answer 9

Correct, cot = cos/sin

Answer 10

and cos and sin are both 45 right?

Answer 11

no, tHey are BotH 1

Answer 12

No, cos45 = sin45 = sqrt2/2

Answer 13

When you divide them, you get 1.

Answer 14

YEaH wHat He said

Answer 15

so its (sqrt2/2)/(sqrt2/2)

Answer 16

which becomes sqrt/2 * 2/sqrt

Answer 17

which then cancels to 1 right?

Answer 18

NO, it is \[\frac{ \frac{ 1 }{ \sqrt{2} } }{ \frac{ 1 }{ \sqrt{2} } }=\frac{ \cos 45 }{ \sin 45 }=\cot 45\]

Answer 19

huh

Answer 20

@agent0smith could u explain

Answer 21

Yes, cot45 = 1, just like tan45=1.

Answer 22

how do u get there though

Answer 23

i need to see hoe u got there

Answer 24

Get cos and sine from the triangle (or use tan):

cos45 = 1/sqrt2
sin45 = 1/sqrt2

cot45 = 1/tan45

tan45 = (1/sqrt2)/(1/sqrt2) = 1

so cot45 = 1/tan45 = 1/1 =

Answer 25

why 1/sqrt 2

Answer 26

Because cos is adj/hyp... look at the triangle.

Answer 27

why r the side lengths 1

Answer 28

cos45 = 1 / sqrt2
sin45 = 1 / sqrt2

cot45 = cos / sin
cot54 = (1/sqrt2)/(1/sqrt2) = 1/1 = 1

Answer 29

is that a good explanation

Answer 30

The side lengths have to both be 1 with a right angle so that it's isosceles, and will have 45 degree angles.