Question

Sinx=1        5 Найти cos, tg, ctg=?        

Answer 1

sinx=1/5

sin^2x+cos^2x=1

cos^2x=1-sin^2x=1-(1/5)^2=1-1/25=25/25-1/25=24/25

cosx=корен24/25=2корен6/5 

 

tgx=sinx/cosx=(1/5)/(2корен6/5)=1/2корен6

ctgx=cosx/sinx=(2корен6/5)/(1/2корен6)=корен576/5=24/5=4,8

 

Answer 2

To solve this equation, we need to use inverse trigonometric functions. Taking the inverse sine of both sides, we get:

x = arcsin(1) = π/2

Therefore, sin(x) = 1 when x = π/2.

Now, to find the values of cos(x), tan(x), and cot(x), we can use the following trigonometric identities:

cos(x) = cos(π/2 - x) tan(x) = sin(x) / cos(x) cot(x) = 1 / tan(x)

Using these identities, we get:

cos(x) = cos(π/2 - x) = sin(x) = 1 tan(x) = sin(x) / cos(x) = 1/1 = 1 cot(x) = 1 / tan(x) = 1/1 = 1

Therefore, cos(x) = 1, tan(x) = 1, and cot(x) = 1 when sin(x) = 1 and x = π/2.