Question

please help with this problem, I solved through but got it wrong, my answers were: sin = 7root58/58, cos= -3root58/58, and tan= -7/3

Answer 1

`\begin{gathered} \text{Sin }(\alpha)/(2)\text{ = 0.3939} \\ \cos \text{ }(\alpha)/(2)\text{ = }0.9191 \\ \tan \text{ }(\alpha)/(2)\text{ = 0.4286} \end{gathered}`

Explanation:

Given information

`\tan \text{ }\alpha\text{ = }(21)/(20)`

Recall that,

`\tan \text{ }\alpha\text{ = }\frac{opposite\text{ }}{\text{adjacent}}`

This implies that,

The opposite side of the triangle = 21

Adjacent side of the triangle = 20

This can be represented pictorially below as

`The\text{ next step is to find }\alpha`
`\begin{gathered} \tan \text{ }\alpha\text{ = }(21)/(20) \\ \tan \text{ }\alpha\text{ = 1.05} \\ \alpha=tan^(-1)\text{ (1.05)} \\ \alpha\text{ = 46.40}\degree \end{gathered}`
`\text{ since }\alpha\text{ = 46.40, we can now find the following}`
`\begin{gathered} \sin \text{ }(\alpha)/(2) \\ \text{where }\alpha\text{ = 46.40} \\ \sin \text{ }(46.40)/(2) \\ \sin \text{ }(\alpha)/(2)\text{ = 0.3939} \end{gathered}`
`\begin{gathered} \cos \text{ }(\alpha)/(2)\text{ = cos }(46.40)/(2) \\ \cos \text{ }(\alpha)/(2)\text{ = cos }(46.40)/(2) \\ \cos \text{ }(\alpha)/(2)\text{ = cos 23.20} \\ \cos \text{ }(\alpha)/(2)\text{ = 0.9191} \end{gathered}`
`\begin{gathered} \tan \text{ }(\alpha)/(2)\text{ = tan }(46.40)/(2) \\ \tan \text{ }(\alpha)/(2)\text{ = tan }23.20 \\ \tan \text{ }(\alpha)/(2)\text{ = 0.4286} \end{gathered}`