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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) = +- square root of (1 - cos a)/2.

= - square root of [( 1 - cos 45o)/2]
= - square root of [(1 - 0.7071)/2]
= - square root of 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.