Question

How do I find the following trigonometric ratios:1. Cos theta2.Cos alpha For this image below

Answer 1

from the diagram above, we can find the various trigonometric ratios using a system call SOHCATOA

`\begin{gathered} \text{SOHCAHTOA} \\ \text{ sin}\theta=(opposite)/(hypothenus) \\ \text{cos}\theta=(adjacent)/(hypothenus) \\ \text{tan}\theta=(opposite)/(adjacent) \end{gathered}`
`\begin{gathered} \text{hypothenus}=4.36 \\ \text{opposite}=2.46 \\ \text{adjacent}=3.6 \end{gathered}`

so, we can go ahead and plug in the variables into each expression

`\begin{gathered} \text{ sin}\theta=(opp)/(hyp) \\ \text{ sin}\theta=(2.46)/(4.36) \\ \text{ sin }\theta=0.5642 \\ \text{take the sine inverse } \\ \theta=\sin ^(-1)0.5642 \\ \theta=34.35^0 \end{gathered}`
`\begin{gathered} \text{cos}\theta=(adj)/(hyp) \\ \text{cos}\theta=(3.6)/(4.36) \\ cos\theta=0.8257 \\ \theta=\cos ^(-1)0.8257 \\ \theta=34.35^0 \end{gathered}`
`\begin{gathered} \text{cos}\alpha=\cos (90-\theta) \\ \text{cos}\alpha=\cos (90-34.35) \\ \text{cos}\alpha=\cos 55.65 \\ \text{cos}\alpha=55.65^0 \end{gathered}`