Question

If $\cos \theta = \dfrac{15}{17}$, then find the value of $\sin \theta$.

Hint:

Use $\sin^2 \theta + \cos^2 \theta = 1$ to find one trigonometric ratio when the other is given.

Answer 1

Step 1: Use the trigonometric identity.
\[ \sin^2 \theta + \cos^2 \theta = 1 \]
Step 2: Substitute the given value.
\[ \sin^2 \theta + \left(\dfrac{15}{17}\right)^2 = 1 \Rightarrow \sin^2 \theta + \dfrac{225}{289} = 1 \] \[ \sin^2 \theta = \dfrac{289 - 225}{289} = \dfrac{64}{289} \Rightarrow \sin \theta = \dfrac{8}{17} \]
Step 3: Conclusion.
Hence, $\sin \theta = \dfrac{8}{17}$.