Question

Simplify
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAwHYpvLFT3W2B.r1xwq7VWktfz8iMLm8IuoB/19809088,B86/Assets/assessmentimages/alg%202%20pt%202%20u2l7%201.jpg

sin θ

csc θ

tan θ

sec θ

Answer 1

@jim_thompson5910

Answer 2

hint: cot = cos/sin

Answer 3

sin?

Answer 4

@jim_thompson5910

Answer 5

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\cot(\theta)\div\cos(\theta)\]

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{\sin(\theta)}\div\frac{\cos(\theta)}{1}\]

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{\sin(\theta)}\times\frac{1}{\cos(\theta)}\]

What happens next?

Answer 6

cos 0= sin1

Answer 7

?

Answer 8

A pair of terms will cancel. Which pair of terms?

Answer 9

cos

Answer 10

yes, so we'd have

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{\sin(\theta)}\times\frac{1}{\cos(\theta)}\]

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\frac{\cancel{\cos(\theta)}}{\sin(\theta)}\times\frac{1}{\cancel{\cos(\theta)}}\]

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\frac{1}{\sin(\theta)}\]

\[\Large \frac{\cot(\theta)}{\cos(\theta)}=\csc(\theta)\]

Answer 11

ok so answer b

Answer 12

`ok so answer b`
correct