If sin α = 3/5, then tan α = ?

Concept:

Trigonometric functions:

• Trigonometric functions also known as circular functions can be simply defined as the functions of an angle of a triangle.
• It means that the relationship between the angles and sides of a triangle is given by these trigonometric functions.
• The basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

Tan θ:

• The tan α is the ratio of the Opposite side to the Adjacent, where α is one of the acute angles.
• \(tan α=\frac{\sin α}{\cos α}\)
• tan 0°  = 0
• tan 30° = \(\frac{1}{\sqrt{3}}\)
• tan 45° = 1
• tan 60° = \(\sqrt{3}\)
• tan 90° = ∞

Calculation:

Given:

∵ sin α = 3/5

And sin² α + cos² α = 1

⇒ cos2 α = \(1-(\frac{3}{5})^2\) = \(1~-~\frac{9}{25}~=~\frac{16}{25}\)

⇒ cos α = \(\frac{4}{5}\)

∵ tan α = \(\frac{\sin α}{\cos α}\) = \(\frac{3}{4}\)

Additional Information
tan α:

• The tan α is the ratio of the opposite side to the adjacent side.

tan α = \(\frac{AC}{BC}\)

sin α:

• The sin α is the ratio of the opposite side to the hypotenuse.

sin α = \(\frac{AC}{AB}\)

cos α:

• The cos α is the ratio of the adjacent side to the hypotenuse, where α is one of the acute angles.

cos α = \(\frac{BC}{AB}\)