Question

Find the exact value of each of the remaining trigonometric functions of e.tan 0 = 7/25 0 in Quadrant II

Answer 1

Concept

Trigonometric functions are

`\sin \theta\text{, }\cos \theta\text{ and }\tan \theta`
`\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \cos \theta\text{ = }\frac{Adjacent}{\text{Hypotenuse}} \\ \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \end{gathered}`

Step-by-step

Draw a triangle and find the length of the hypotenuse using the tangent angle.

The apply Pythagoras theorem below to find the length of the hypotenuse.

`\begin{gathered} \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ \text{Opposite = 7} \\ \text{Adjacent = 25} \\ \text{Substitute in the equation to calculate the unknown length.} \\ 7^2+25^2=Hypotenuse^2 \\ 49+625=Hypotenuse^2 \\ L^2\text{ = 694} \\ Take\text{ square root of both sides.} \\ L\text{ = }\sqrt[]{694} \\ Hypotenuse\text{ = 26.3} \\ \text{Hypotenuse = 26} \end{gathered}`

The remaining trigonometric functions are

`\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ =(7)/(26) \\ \cos \theta\text{ = }\frac{Adjacent}{\text{Hypotenuse}} \\ =\text{ }(25)/(26) \end{gathered}`