Question

I need to find out what sine cosine and cotangent is, if this is my reference angle in the picture

Answer 1

We will use the following trigonometric identities

`\begin{gathered} \tan \Theta=(sin\Theta)/(\cos \Theta) \\ \cot \Theta=(1)/(\tan \Theta) \end{gathered}`

Using these identities we can identify

`\begin{gathered} \tan \Theta=(12)/(5) \\ \sin \Theta=12 \\ \cos \Theta=5 \\ \cot \Theta=(1)/((12)/(5))=(5)/(12) \end{gathered}`
`\begin{gathered} \Theta=\tan ^(-1)(2.4) \\ \Theta=67.38º \\ \sin \Theta=0.92 \\ \cos \Theta=0.38 \end{gathered}`
`\begin{gathered} \tan \Theta=\frac{opposite}{\text{adjacent}}^{} \\ \text{opposite}=12 \\ \text{adjacent}=5 \\ \text{hippotenuse=}\sqrt[\square]{12^2+5^2} \\ \text{hippotenuse=}13 \end{gathered}`
`\begin{gathered} \sin \Theta=(12)/(13) \\ \cos \Theta=(5)/(13) \end{gathered}`