Question

Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.

Answer 1

Step 1

The terminal side, containing point (-3, 4) is located in Quadrant 2.

sine is positive

cosine and tangent are both negative.

Step 2

Draw a diagram to illustrate the information

Step 3

`\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }√(25) \\ \text{d = 5} \end{gathered}`

Step 4:

`\begin{gathered} sine\text{ = }(Opposite)/(Hypotenuse) \\ Sin\theta\text{ = }(4)/(5) \end{gathered}`
`\begin{gathered} Cosine\text{ = }(Adjacent)/(Hypotenuse)\text{ = }(x)/(d) \\ Cos\theta\text{ = }(-3)/(5) \end{gathered}`
`\begin{gathered} tangent\text{ = }(Opposite)/(Adjacent)\text{ = }(y)/(x) \\ tan\theta\text{ = }(-4)/(3) \end{gathered}`

Final answer

`\begin{gathered} sin\theta\text{ = }(4)/(5) \\ cos\theta\text{ = }(-3)/(5) \\ tan\theta=(-4)/(3) \end{gathered}`