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(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(1)/(2))^\circ\approx 0.566`

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

`\sin (90-55(1)/(2))^\circ\approx 0.566`

`\sin (90-(110+1)/(2))^\circ\approx 0.566`

`\sin (90-(111)/(2))^\circ\approx 0.566`

Taking LCM, we get

`\sin ((180-111)/(2))^\circ\approx 0.566`

`\sin ((69)/(2))^\circ\approx 0.566`

`\sin (34(1)/(2))^\circ\approx 0.566`

Therefore, the angle
`34(1)/(2)` degrees has a sine of approximately 0.566.