Using a trigonometric identity, the cosine of the angle is given as follows:
[tex]\cos{\theta} = \frac{60}{61}[/tex]
What is the trigonometric identity that relates the sine and the cosine of an angle?
It is given by:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, the sine is:
[tex]\sin{\theta} = \frac{11}{61}[/tex]
Then:
[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]
[tex]\cos^2{\theta} = 1 - \left(\frac{11}{61}\right)^2[/tex]
[tex]\cos^2{\theta} = \frac{3600}{3721}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{3600}{3721}}[/tex]
On quadrant I, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{60}{61}[/tex]
More can be learned about trigonometric identities at https://brainly.com/question/24496175
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