Answers: 1
 because that is the range of the inverse cosine funcition.![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](/tpl/images/0256/6594/ad819.png)
lies either in the 1st or the 2nd quadrant. So 
is a positive number:![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](/tpl/images/0256/6594/39a8e.png)
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