Answer :
Given:
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
To find:
The angle, in degrees, that has a sine of approximately 0.566.
Solution:
We know that,
[tex]\sin(90^\circ-x)=\cos x[/tex]
We have,
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
Using the above trigonometric identity, it can be written as:
[tex]\sin (90-55\dfrac{1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{110+1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{111}{2})^\circ\approx 0.566[/tex]
Taking LCM, we get
[tex]\sin (\dfrac{180-111}{2})^\circ\approx 0.566[/tex]
[tex]\sin (\dfrac{69}{2})^\circ\approx 0.566[/tex]
[tex]\sin (34\dfrac{1}{2})^\circ\approx 0.566[/tex]
Therefore, the angle [tex]34\dfrac{1}{2}[/tex] degrees has a sine of approximately 0.566.