Question

If sinx is approximately 0.2588, what is the measurement of x to the nearest degree? Approximately, what is the cosine of the angle that is complementary to x?

Answer 1

$\bf sin(x)\approx 0.2588\implies \measuredangle x \approx sin^{-1}(0.2588)\\\\ -----------------------------\\\\ sin\left(\frac{\pi}{2}-{{ \theta}}\right)=cos({{ \theta}})\qquad cos\left(\frac{\pi}{2}-{{ \theta}}\right)=sin({{ \theta}})\leftarrow \begin{array}{llll} complementary\\ angles \end{array}\\\\ -----------------------------\\\\ thus\qquad cos\left( \frac{\pi }{2}-x \right)=sin(x)\approx 0.2588$

Answer 2

75 degrees;0.2588. The compliant of 15 degrees is 75 degrees.