Which numbers can be placed in the blank to make the value of this expression a negative number? (-16) -

Mathematics

1 answer:

Genrish500 [490]3 years ago

3 0

Answer:

All numbers greater than -16.

Step-by-step explanation:

Hello!

To keep this expression negative, we can subtract a positive number (numbers greater than or equal to 0), to give us an even smaller negative number.

Another option is to add a negative number so that the value is still negative. We can add any number that is larger than -16.

Answer: All numbers greater than -16

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$\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}$

$\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}$