Find a cofunction with the same value as the given expression.
csc 35°

Verified step by step guidance

1. Recall the cofunction identity: \( \csc(\theta) = \sec(90^\circ - \theta) \).
2. Identify the given angle \( \theta = 35^\circ \).
3. Substitute \( \theta = 35^\circ \) into the cofunction identity: \( \csc(35^\circ) = \sec(90^\circ - 35^\circ) \).
4. Calculate \( 90^\circ - 35^\circ \) to find the angle for the secant function.
5. Express the cofunction: \( \csc(35^\circ) = \sec(55^\circ) \).

Key Concepts

Cofunction Identities

Cofunction identities in trigonometry relate the values of trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This principle allows us to find equivalent trigonometric values by using angles that add up to 90 degrees.

Cosecant Function

The cosecant function, denoted as csc(θ), is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ). Understanding this relationship is crucial for finding cofunctions, as it helps in determining the sine value needed to find the corresponding cosecant value.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In the context of trigonometric functions, knowing the complementary angle allows us to apply cofunction identities effectively. For instance, to find a cofunction for csc(35°), we can use the complementary angle 55° (90° - 35°) to relate it to sin(55°).