Find the value of sine nine hundred twenty-two point five degrees
Question:
Find the value of sin 922.5 degrees
Solution:
- sin 922.5o
- = sin (2 × 360o + 202.5o)
Using the formula, sin (k × 360o + a) = sin a, in which k is an integer.
- = sin 202.5o
- = sin (180o + 22.5o)
Using the formula, sin (180o + a) = - sin a
- = - sin 22.5o
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 45o)/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 922.5o lies in Quadrant3, so the value of sin 922.5o is a negative value.