Question

hello can yoy help with this plane trigonometry question and in the question turn it into radians and thank you for your time for helping me

Answer 1

Answer:

The angle between 0 and 2 pie that is coterminal to the given angle is;

$\frac{6}{7}\pi$

Explanation:

We want to find the angle between 0 and 2 pie that is coterminal to;

$\frac{34}{7}\pi$

Angles that are coterminal with the given angle can be calculated using the formula;

$x+n2\pi=\frac{34}{7}\pi$

Where n=1,2,3...

and x is the coterminal angle.

At n = 1;

$\begin{gathered} x+2\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-2\pi \\ x=\frac{34}{7}\pi-\frac{14}{7}\pi \\ x=\frac{20}{7}\pi \end{gathered}$

at n=2;

$\begin{gathered} x+2(2\pi)=\frac{34}{7}\pi \\ x+4\pi=\frac{34}{7}\pi \\ x=\frac{34}{7}\pi-4\pi \\ x=\frac{34}{7}\pi-\frac{28}{7}\pi \\ x=\frac{6}{7}\pi \end{gathered}$

At n=2;

The value of x is between 0 and 2pie;

So, the angle between 0 and 2 pie that is coterminal to the given angle is;

$\frac{6}{7}\pi$