Question

The value of sin theta increase as theta increases . true or false and justify your answer.

Answer 1

$sin {0}^{o } = 0 \\ sin {30}^{o} = \frac{1}{2} = 0.5 \\ sin {45}^{o} = \frac{1}{ \sqrt{2} } = 0.707(approx) \\ sin {60}^{o} = \frac{ \sqrt{3} }{2} = 0.866(approx) \\ and \: sin {90}^{o} = 1 \\ thus \: the \: given \: statement \: is \\ true.$

Answer 2

true

The value of sin θ rises from 0 to 1 as theta climbs from 0 to 90. The sine function, denoted as sin, is equivalent to the ratio of the opposite side of the reference angle  by the hypotenuse, or long side, of the triangles in the setting of a right angle. Because Sin = Perpendicular/Hypotenuse and a perpendicular is never longer than the hypotenuse, Sin can never be more than 1. When theta is greater than 180 degrees, the value of sin turns negative.