Question 12 Marks
If $\sin \theta = \frac{11}{61}$, find the values of $\cos \theta$ using trigonometric identity.
Answer
View full question & answer→Using the identity $\sin^{2}\theta + \cos^{2}\theta = 1$:
$(\frac{11}{61})^{2} + \cos^{2}\theta = 1$
$\frac{121}{3721} + \cos^{2}\theta = 1$
$\cos^{2}\theta = 1 - \frac{121}{3721}$
$\cos^{2}\theta = \frac{3721 - 121}{3721} = \frac{3600}{3721}$
$\cos \theta = \frac{60}{61}$
$(\frac{11}{61})^{2} + \cos^{2}\theta = 1$
$\frac{121}{3721} + \cos^{2}\theta = 1$
$\cos^{2}\theta = 1 - \frac{121}{3721}$
$\cos^{2}\theta = \frac{3721 - 121}{3721} = \frac{3600}{3721}$
$\cos \theta = \frac{60}{61}$
