Respuesta :
We have to calculate the cosine of an angle using the value of its sine. For this purpose we can use the following relation that is met for any angle:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Then, the cosine is given by:
[tex]\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \\ \cos \theta=\sqrt[]{1-\sin^2\theta} \\ \lvert\cos \theta\rvert=\sqrt[]{1-(\frac{1}{4})^2}=\sqrt[]{1-\frac{1}{16}}=\sqrt[]{\frac{15}{16}} \end{gathered}[/tex]This means that the cosine is either:
[tex]\sqrt[]{\frac{15}{16}}[/tex]or:
[tex]-\sqrt[]{\frac{15}{16}}[/tex]Since the angle theta is between 90° and 180° then its cosine must be a negative number then:
[tex]\cos \theta=-\sqrt[]{\frac{15}{16}}[/tex]