Given:
θ is an angle in standard position.
Its terminal side passes through the point (6,1).
To find:
The exact value of secθ in simplest radical form.
Solution:
If θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:
[tex]\sec\theta =\dfrac{Hypotenuse}{Base}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{x^2+y^2}}{x}[/tex]
It is given that θ is an angle in standard position and its terminal side passes through the point (6,1), then the exact value of secθ is:
[tex]\sec\theta =\dfrac{\sqrt{6^2+1^2}}{6}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{36+1}}{6}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{37}}{6}[/tex]
Therefore, the exact value of secθ is [tex]\dfrac{\sqrt{37}}{6}[/tex].
