Find the value of sine nine hundred twenty-two point five degrees

Question:

Find the value of sin 922.5 degrees

Solution:

sin 922.5^o

= sin (2 × 360^o + 202.5^o)

Using the formula, sin (k × 360^o + a) = sin a, in which k is an integer.

= sin 202.5^o

= sin (180^o + 22.5^o)

Using the formula, sin (180^o + a) = - sin a

= - sin 22.5^o

Because 22.5 degrees is half of 45 degrees, so we use the half angle formula, sin (a/2) = +- Sqrt (1 - cos a)/2.

= - Sqrt [( 1 - cos 45^o)/2]

= - Sqrt [(1 - 0.7071)/2]

= - Sqrt 0.1465

= - 0.38275

Therefore, the value of sin 922.5 degrees is -0.38275. Please watch the video for more details.

Note: the terminal side of the angle 922.5^o lies in Quadrant3, so the value of sin 922.5^o is a negative value.