Question

If cosine = 1/7 in quadrant 1, find tangent

Answer 1

What we know from the problem:

• Cosine = Adjacent/Hypotenuse = 1/7

• If you make a triangle in the first quadrant all the sides are positive

therefore tangent will be positive.

• So we know that:

Adjacent Side = 1

Hypotenuse Side = 7

We need to find out:

Opposite Side = b

Using the Pythagorean Theorem: a² + b² = c²

1² + b² = 7²

b = 4√3

Lastly:

Tangent = Opposite/Adjacent

4√3 ÷ 1 = 4√3

Tangent = 4√3

Answer 2

First, we can use the Pythagorean identity to find the value of sine:

sin^2 θ + cos^2 θ = 1

sin^2 θ + (1/7)^2 = 1

sin^2 θ = 1 - (1/49)

sin^2 θ = 48/49

sin θ = √(48/49) = (4√3)/7 (since sine is positive in quadrant 1)

Now we can use the definition of tangent:

tan θ = sin θ / cos θ

tan θ = [(4√3)/7] / (1/7)

tan θ = 4√3

Therefore, the tangent of the angle is 4√3.