Final answer:
To express tan(52 degrees) in terms of sine and cosine, use the identity tan(theta) = sin(theta) / cos(theta) and write it as sin(52 degrees) / cos(52 degrees).
Step-by-step explanation:
The tangent of an angle, in terms of sine and cosine, is defined as the ratio of the sine of the angle to the cosine of the angle. For a given angle θ, the tangent is represented as tan(θ) = sin(θ) / cos(θ). Applying this definition to the specific angle 52 degrees, the tangent of 52 degrees can be expressed as tan(52°) = sin(52°) / cos(52°). This ratio provides a relationship between the sine and cosine functions for the angle 52 degrees.
In trigonometry, understanding these relationships helps express one trigonometric function in terms of others, enabling the simplification of expressions and the exploration of geometric and functional properties related to angles and triangles.