evaluate. write your answers in simplified, rationalized forms. do not round.\nsin 60° =\ncos 60° =\ntan 60° =

Explanation:

Step1: Recall sine - value of 60 degrees

In a 30 - 60 - 90 right - triangle, if the hypotenuse $c = 2$, the side opposite the 60 - degree angle $a=\sqrt{3}$ and the side opposite the 30 - degree angle $b = 1$. By the definition of sine $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, so $\sin60^{\circ}=\frac{\sqrt{3}}{2}$.

Step2: Recall cosine - value of 60 degrees

By the definition of cosine $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In a 30 - 60 - 90 right - triangle with hypotenuse $c = 2$ and the side adjacent to the 60 - degree angle $b = 1$, so $\cos60^{\circ}=\frac{1}{2}$.

Step3: Recall tangent - value of 60 degrees

By the definition of tangent $\tan\theta=\frac{\sin\theta}{\cos\theta}$. Since $\sin60^{\circ}=\frac{\sqrt{3}}{2}$ and $\cos60^{\circ}=\frac{1}{2}$, then $\tan60^{\circ}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$.

Answer:

$\sin60^{\circ}=\frac{\sqrt{3}}{2}$, $\cos60^{\circ}=\frac{1}{2}$, $\tan60^{\circ}=\sqrt{3}$