Find the secant of an angle on the unit circle for $ heta = 45^{circ}$.
Answer 1
Lucas Brown
To find the secant of the angle $\theta = 45^{\circ}$ on the unit circle, we use the relationship between secant and cosine.
The secant of an angle is the reciprocal of its cosine:
$\sec(\theta) = \frac{1}{\cos(\theta)}$.
For $\theta = 45^{\circ}$, the cosine value is $\cos(45^{\circ}) = \frac{\sqrt{2}}{2}$.
Therefore,
$\sec(45^{\circ}) = \frac{1}{\cos(45^{\circ})} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}$.
So, the secant of $45^{\circ}$ is $\sqrt{2}$.
Answer 2
Mia Harris
To determine the secant of $45^{circ}$ on the unit circle, recall that secant is the reciprocal of cosine:
$sec( heta) = frac{1}{cos( heta)}$.
We know that $cos(45^{circ}) = frac{sqrt{2}}{2}$.
Thus,
$sec(45^{circ}) = frac{1}{frac{sqrt{2}}{2}} = sqrt{2}$.
Hence, the secant of $45^{circ}$ is $sqrt{2}$.
Answer 3
Matthew Carter
For $ heta = 45^{circ}$,
$sec(45^{circ}) = frac{1}{cos(45^{circ})}$.
Given $cos(45^{circ}) = frac{sqrt{2}}{2}$,
$sec(45^{circ}) = sqrt{2}$.
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