數學問題! Trigonometric Relations!

tan Θ= 4 = 4/1

Let AB = 4 and BC = 1

(draw a right-angled triangle named ABC with angle B = 90° and angle C = Θ. Mark side AB with a length of 4 and side BC with a length of 1.)

AC (square) = AB (square) + BC (square) (Pyth.thm)
AC (square) = 4 (square) + 1 (square)
AC (square) = 17
AC = √17

sinΘ = AB / AC
sinΘ = 4 / √17
sinΘ = (4√17)/17

cosΘ = BC / AC
cosΘ = 1 / √17
cosΘ = (1√17)/17




* (square) 代表 自乘二次
* triangle and its sides can be named in other ways (e.g. XYZ, GHI, etc.)

Let X be the hypotaneous(斜邊) of this triangle

tanΘ=4/1
=4

所以
X^2 = √(4^2 + 1^2 )
X = √17

所以sinΘ=4/√17
=4√17/17


cosΘ=1/ √17
= √17/17

tan Θ= 4

sinΘ = 4/√17 (= 4√17/17)
cosΘ = 1/√17 (=√17/17)