If sin (theta°) = 0.5, and we know that cos (theta°) < 0, then what is the smallest possible positive value of theta?

150°

Step-by-step explanation:

It is given that CosФ < 0 i. e CosФ is negative.

Therefore, the minimum the value of Ф for which CosФ <0 will be in the second quadrant i. e 90° < Ф < 180°.

Now it is also given that, Sin Ф = 0.5 {the value of SinФ is positive because Sin value is positive in second quadrant.}

⇒ Ф = 180° - Sin⁻¹ (0.5) = 180°-30° = 150° (Answer)