# Thread: Equivalent Expression in terms of Related Acute Angle [Year 11 Advanced Functions]

1. ## Equivalent Expression in terms of Related Acute Angle [Year 11 Advanced Functions]

Here's the question:
State an equivalent expression for $\displaystyle sec(7*pi/6)$ in terms of the related acute angle.

The answer is $\displaystyle sec(5*pi/6)$

What is the step-by-step solution. Thanks!

2. Originally Posted by essaymasters
Here's the question:
State an equivalent expression for $\displaystyle sec(7*pi/6)$ in terms of the related acute angle.

The answer is $\displaystyle sec(5*pi/6)$

What is the step-by-step solution. Thanks!
the reference angle for $\displaystyle \frac {7 \pi}6$ is $\displaystyle \frac {\pi}6$.

$\displaystyle \frac {7 \pi}6$ is in the 3rd quadrant, and so we get a negative answer. since the secant function is negative in the second and third quadrant, the other reference angle that we could take is $\displaystyle \frac {5 \pi}6$

draw the unit circle at draw these angles in to see what's going on. note that $\displaystyle \frac {7 \pi}6$ and $\displaystyle \frac {5 \pi}6$ make an angle of $\displaystyle \frac {\pi}6$ with the negative x-axis.

3. Cheers Jhevon!

So what I should do is pick an angle on a valid quadrant that has the same related angle, yeah?