Rewrite cscθ/cotθ in terms of sine and cosine.

Question

Rewrite cscθ/cotθ in terms of sine and cosine. Simplify your answer. 

Answer 1

you should be able to do this, simply by following instructions and using the definition that cosecant equals the reciprocal of sine, and  cotangent = cosine divided by sine.  also, remember that to divide by a fraction, you multiply by its reciprocal.

 

now go for it!

Answer 2

To write csc(θ) / cot(θ) in terms of sin and cos, we can use the trig identities. We know that there is a reciprocal identity for csc(θ) which is 1 / sin θ and there is a quotient identity that says cot θ = cos(θ) / sin(θ) so we can replace csc(θ) with 1 / sin(θ) and cot(θ) with cos(θ)/sin(θ). So, it becomes:

(1 / sin(θ)) ÷ (cos(θ) / sin(θ))

= (1 / sin(θ)) × (sin(θ) / cos(θ)) Applied "Keep Change Flip" since we were dividing fractions

= (sin(θ)) / (sin(θ)cos(θ)) We can further simplify by canceling out sin(θ) in the fraction

= 1 / cos(θ)

So, our simplified answer in terms of cos(θ) is 1 / cos(θ).

Answer 3

cscθ/cotθ

(1/sinθ)÷(cosθ/sinθ)

(1/sinθ)*(sinθ/cosθ)

simplify by cancelling the sinθ's

1/cosθ