Answer:
[tex]\begin{gathered} sine(45)=\frac{\sqrt{2}}{2} \\ cosine(45)=\frac{\sqrt{2}}{2} \end{gathered}[/tex]
Step-by-step explanation:
The hypotenuse of a reference triangle that lies on the unit circle is the radius of the unit circle. Therefore, if it has a radius of 3 and a reference triangle of 45 degrees.
Remember that sine and cosine are represented by the following equations:
[tex]\begin{gathered} sin(angle)=\frac{opposite}{hypotenuse} \\ cos(angle)=\frac{adjacent\text{ }}{hypotenuse} \end{gathered}[/tex]
Now, for the following circle and the reference triangle:
[tex]\begin{gathered} \text{ sin\lparen45\rparen=}\frac{opposite}{3} \\ \text{ opposite=3*sin\lparen45\rparen} \\ opposite=\frac{3\sqrt{2}}{2} \\ \\ \text{ cos\lparen45\rparen=}\frac{\text{ adjacent}}{3} \\ \text{ adjacent=}\frac{3\sqrt{2}}{2} \end{gathered}[/tex]
Hence, for the sin and cosine:
[tex]\begin{gathered} sine(45)=\frac{\sqrt{2}}{2} \\ cosine(45)=\frac{\sqrt{2}}{2} \end{gathered}[/tex]
