Question

The cosine of 55 1/2 degrees is approximately 0.566. What angle, in degrees, has a sine of approximately 0.566?

Answer 1

Given:

$\cos (55\dfrac{1}{2})^\circ\approx 0.566$

To find:

The angle, in degrees, that has a sine of approximately 0.566.

Solution:

We know that,

$\sin(90^\circ-x)=\cos x$

We have,

$\cos (55\dfrac{1}{2})^\circ\approx 0.566$

Using the above trigonometric identity, it can be written as:

$\sin (90-55\dfrac{1}{2})^\circ\approx 0.566$

$\sin (90-\dfrac{110+1}{2})^\circ\approx 0.566$

$\sin (90-\dfrac{111}{2})^\circ\approx 0.566$

Taking LCM, we get

$\sin (\dfrac{180-111}{2})^\circ\approx 0.566$

$\sin (\dfrac{69}{2})^\circ\approx 0.566$

$\sin (34\dfrac{1}{2})^\circ\approx 0.566$

Therefore, the angle $34\dfrac{1}{2}$ degrees has a sine of approximately 0.566.