Question

Which equation could be used to find the value of a degree or Ф in trigonometry?

a. sin(Ф) = 1/cos(Ф)
b. tan(Ф) = 1/cot(Ф)
c. cot(Ф) = 1/tan(Ф)
d. cos(Ф) = 1/sin(Ф)

Answer 1

The correct equation to find the value of a degree or Ф in trigonometry is cot(Ф) = 1/tan(Ф), representing the reciprocal identity between tangent and cotangent.

Step-by-step explanation:

The correct equation from the options provided to find the value of a degree or Ф in trigonometry is c. cot(Ф) = 1/tan(Ф). This equation represents one of the fundamental relationships in trigonometry, which is known as the reciprocal identity.

The reciprocal identities show the inverse relationships between the sine, cosine, tangent, cotangent, secant, and cosecant functions. For example, the cotangent of an angle is the reciprocal of the tangent of that angle, which is shown by the formula cot(Ф) = 1/tan(Ф). Option b is also correct, as tan(Ф) = 1/cot(Ф), which is another way to express this reciprocal relationship.