If 𝗌𝗂𝗇 θ=45, then what is the 𝖼𝗈𝗌(90°−θ)?

Question

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Answer 1

Use the following identities:

 

cosθ = sin(90° - θ)

 

sinθ = cos(90° - θ)

 

Then

 

cos(90° - θ) = sinθ = 45°

Answer 2

Definition of
sin (x) = (side opposite angle x)/(hypotenuse)

Definition of
cos(90^∘-x) =(side adjacent to angle (90^∘−x))/(hypotenuse)

but, (side opposite angle x) = (side adjacent to angle (90^∘−x)

Therefore,

sin(x)=cos(90^∘−x)

 

So, if If 𝗌𝗂𝗇 θ=45, 𝖼𝗈𝗌(90°−θ) = 𝗌𝗂𝗇 θ=45^∘