Use a ratio identity to find tan(θ) if given the following.

sin=6/sq rt 37 and cos 1/sq rt 37

sinØ = 6/√37 , cosØ = 1/√37

Ø must be in quad I, and my triangle has x=1, y=6 and r= √37
tanØ = 6/1 = 6

To find the value of tan(θ), we can use the identity tan(θ) = sin(θ) / cos(θ).

Given that sin(θ) = 6/sqrt(37) and cos(θ) = 1/sqrt(37), we can substitute these values into the identity:

tan(θ) = sin(θ) / cos(θ)
= (6/sqrt(37)) / (1/sqrt(37))
= (6/sqrt(37)) * (sqrt(37)/1)
= (6 * sqrt(37)) / (sqrt(37))
= 6

Therefore, tan(θ) is equal to 6.

To find the value of tan(θ) given the values of sin and cos, we can use the identity:

tan(θ) = sin(θ) / cos(θ)

Given sin(θ) = 6/√37 and cos(θ) = 1/√37, we can substitute these values into the ratio identity:

tan(θ) = (6/√37) / (1/√37)

To divide fractions, we can multiply the numerator by the reciprocal of the denominator:

tan(θ) = (6/√37) * (√37/1)

The square root of 37 cancels out:

tan(θ) = (6/1) * 1

Therefore, tan(θ) = 6.