Question

What is the exact value of sin 45° ?

enter your answer, as a simplified fraction.

Answer 1

Look at the picture.

Use the Pythagorean theorem:

`b^2=a^2+a^2\\\\b^2=2a^2\to b=√(2a^2)\\\\b=√(a^2)\cdot\sqrt2\\\\b=a\sqrt2`

`\sin\theta=(opposite)/(hypotenuse)\\\\\theta=45^o,\ opposite=a,\ hypotenuse=a\sqrt2`

substitute

`\sin45^o=(a)/(a\sqrt2)=(1)/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)=(\sqrt2)/(2)`

Answer:
`\sin45^o=(\sqrt2)/(2)`