The exact value is
<span>sin<span>(arccos<span>(<span>3/4</span>)</span>)</span></span>The equation for cosine is <span>cos<span>(A)</span>=<span>AdjacentHypotenuse</span></span>. The inside trig function is <span>arccos<span>(<span>3/4</span>)</span></span>, which means <span>cos<span>(A)</span>=<span>3/4</span></span>. Comparing <span>cos<span>(A)</span>=<span>AdjacentHypotenuse</span></span> with <span>cos<span>(A)</span>=<span>3/4</span></span>, find <span>Adjacent=3</span> and <span>Hypotenuse=4</span>. Then, using the pythagorean theorem, find <span>Opposite=<span>√7</span></span>.<span>Adjacent=3</span><span>Opposite=<span>√7</span></span><span>Hypotenuse=4</span>Substitute in the known variables for the equation <span>sin<span>(A)</span>=<span>OppositeHypotenuse</span></span>.<span>sin<span>(A)</span>=<span><span>√7</span> over 4</span></span>Simplify.<span><span>√7</span><span> over 4</span></span>
