Respuesta :

[tex]\begin{gathered} \tan \text{ 60}\degree\text{ = }\frac{\sin\text{ 60}\degree}{\cos\text{ 60}\degree} \\ or \\ \tan \text{ 60}\degree\text{ = }\frac{\text{cos(90 - 60)}\degree}{\text{sin(90 - 60)}\degree} \end{gathered}[/tex] Explanation:[tex]\begin{gathered} 5)\text{ Given: tan60}\degree \\ To\text{ write in terms of sine and/or cosine} \end{gathered}[/tex]

We need to find the relationship between sine, cosine and tangent

[tex]In\text{ trigonometry, tan }\theta\text{ = }\frac{\sin \theta\text{ }}{\cos \text{ }\theta}[/tex][tex]\begin{gathered} In\text{ this case }\theta\text{= 60}\degree \\ We\text{ can replace our }\theta\text{ with 60}\degree \\ \tan \text{ 60}\degree\text{ = }\frac{\sin\text{ 60}\degree}{\cos\text{ 60}\degree} \end{gathered}[/tex][tex]\begin{gathered} \sin \theta\text{ = }cos(90\text{ - }\theta) \\ \sin \text{ 60 = cos(90 - 60)} \\ \\ \cos \theta\text{ = }\sin (90\text{ - }\theta) \\ cos\text{ 60 = sin(90 - 60)} \\ \\ \tan \text{ 60}\degree\text{ = }\frac{\sin\text{ 60}\degree}{\cos\text{ 60}\degree}\text{ = }\frac{\text{cos(90 - 60)}\degree}{\text{sin(90 - 60)}\degree} \end{gathered}[/tex]