Question

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Answer 1

option B

Cos theta is positive and sin theta is negative in quadrant IV

$Cos \ \theta =\dfrac{4}{5}=\dfrac{adjacent \ side}{hypotenuse}$

We have to find opposite side using Pythagorean theorem.

x² + 4² = 5²

x² + 16 = 25

       x² = 25- 16

       x² = 9

       $\sf x =\sqrt{9}\\\\x = 3$

$\sf \ sin \ \theta =\dfrac{opposite \ side}{hypotenuse}\\Sin \ \theta =\dfrac{-3}{5}$