Answer:
The complement of [tex]45\degree[/tex] is [tex]45\degree[/tex].
Step-by-step explanation:
Method 1
From the isosceles right triangle; See diagram in attachment.
[tex]\sin(45\degree)=\frac{x}{x\sqrt{2} }[/tex]
[tex]\sin(45\degree)=\frac{1}{\sqrt{2} }[/tex]
[tex]\sin(45\degree)=\frac{\sqrt{2}}{2 }[/tex]
Also;
[tex]\sin(45\degree)=\frac{x}{x\sqrt{2} }[/tex]
[tex]\cos(45\degree)=\frac{1}{\sqrt{2} }[/tex]
[tex]\cos(45\degree)=\frac{\sqrt{2}}{2 }[/tex]
Hence;
[tex]\cos(45\degree)=\sin(45\degree)[/tex]
Method 2
[tex]\sin(45\degree)=\cos(45\degree)[/tex] because the complement of [tex]45\degree[/tex] is still [tex]45\degree[/tex].
Complementary angles add to [tex]90\degree[/tex].
In general if we have an angle [tex]\theta[/tex], then its complement is [tex](90-\theta)\degree[/tex].
There is a relationship between the sine of an angle,[tex]\theta[/tex] and the cosine of its complement,(90-\theta)\degree[/tex].
The relationship is that,
[tex]\sin(\theta \degree)=\cos((90-\theta)\degree)[/tex].
If [tex]\theta=45\degree[/tex], then
[tex]\sin(45 \degree)=\cos((90-45)\degree)[/tex].
[tex]\Rightarrow \sin(45\degree)=\cos(45\degree)[/tex].
