Question

Rewrite secant theta over tangent theta in terms of sine and cosine.

A) sin(θ)/cos(θ)
B) cos(θ)/sin(θ)
C) tan(θ)
D) cot(θ)

Answer 1

The expression 'secant theta over tangent theta' simplifies to cos(θ)/sin(θ), or the cosecant of theta, which is not listed among the options. Therefore, based on the given choices, the correct answer is B) cos(θ)/sin(θ).

Step-by-step explanation:

To rewrite secant theta over tangent theta in terms of sine and cosine, we first replace secant theta (sec(θ)) with its equivalent in terms of cosine, which is 1/cos(θ), and then we replace tangent theta (tan(θ)) with its equivalent in terms of sine and cosine, which is sin(θ)/cos(θ). Dividing these, we get:

(1/cos(θ)) / (sin(θ)/cos(θ))

When we divide by a fraction, it is the same as multiplying by its reciprocal, so:

(1/cos(θ)) * (cos(θ)/sin(θ))

The cos(θ) in the numerator and denominator cancel out, leaving us with:

1/sin(θ)

Therefore, the expression simplifies to the cosecant of theta, which is csc(θ) or 1/sin(θ), but this option is not listed among the choices.