Understanding Trig Notation: What Does Sin(90°-θ) Mean?

[Feodalherren]

I'm solving some trig functions and ran into a notation that says

Sin(90°-θ)

What does it mean?

I know what Sin θ is and I know that Sin 90° = 1.

 

[Feodalherren]

Just in case it's important, Sin θ=

(2x)(9+4x^2)^(1/2) / (9+4x^2)

 

[ehild]

Do you know how sin(90°-θ) is related to cos(θ)?

What is the full problem?

ehild

 

[Mentallic]

I'm solving some trig functions and ran into a notation that says

Sin(90°-θ)

What does it mean?

I know what Sin θ is and I know that Sin 90° = 1.

θ is some angle (we'll only deal with acute angles here) and then sin θ is the ratio of the opposite side to the hypotenuse in a right-angled triangle with one of its angles as θ. But if you look at that same triangle, you can deduce that the last angle must be
180° - 90° - θ = 90° - θ
because a triangle's angles add up to 180^o.
And now, what is the cosine of that angle? That is, what is cos (90° - θ)? Well, since cos of an angle is the ratio between the adjacent side and the hypotenuse, these are exactly the same sides in the ratio of sin θ, so that means that sin θ = cos (90° - θ)
Can you use a similar procedure to find out what Sin(90°-θ) is?