In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sin 37° csc 37°

Key Concepts

Sine Function

The sine function, denoted as sin(θ), is a fundamental trigonometric function that relates the angle θ of a right triangle to the ratio of the length of the opposite side to the hypotenuse. For example, sin(37°) represents this ratio for a triangle with a 37-degree angle.

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). Therefore, csc(37°) is equal to the reciprocal of sin(37°), which means it represents the ratio of the hypotenuse to the opposite side in a right triangle.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. In this case, using the identity sin(θ) * csc(θ) = 1 can simplify the expression sin(37°) csc(37°) to 1, illustrating the relationship between sine and cosecant.