what csc if cot is 1

Question

Find csc θ if cot θ is 1

Basic Trig Quiz 

Precal / Geometry 

Homework

12th Grade 

Math/ College Math 

Answer 1

let x=θ

cotx=1

cotx=1/tanx=cosx/sinx

cosx/sinx=1

sinx and cosx must be equal

this occurs at ∏/4 when sinx=√2/2 and cosx=√2/2

this also occurs at 5∏/4 when sinx=-√2/2 and cosx=-√2/2

cscx=1/sinx

1/sinx=2/√2=2√2/2=√2

1/sinx=-2/√2=-2√2/2=-√2

so cscx=√2 or -√2 if cotx=1

Answer 2

cot θ = 1 ⇒ 45-45-90 triangle!

sin 45 = √2 / 2

csc 45 = 2√2 / 2