COS[ARCSIN (SIN 3PI/4)]
=COS[ARCSIN (SQRT2/2)]
=COS [PI/4]
= SQRT2/2
To find the value of COS[ARCSIN(SIN(3π/4))], you can follow these steps:
Step 1: Begin by evaluating the innermost function, SIN(3π/4).
The sine function returns the y-coordinate of a point on the unit circle corresponding to a given angle.
For the angle 3π/4, we know that it lies in the second quadrant of the unit circle. In the second quadrant, the y-coordinate is positive, and the x-coordinate is negative.
Since the sine of 3π/4 is positive, we know that SIN(3π/4) = √2/2.
Step 2: Now, evaluate the ARCSIN of √2/2, which is the inverse sine function.
The inverse sine function, ARCSIN, returns the angle whose sine is a given value.
Since SIN(3π/4) = √2/2, we can conclude that ARCSIN(√2/2) = 3π/4.
Step 3: Finally, evaluate the COS of 3π/4.
The cosine function, COS, returns the x-coordinate of a point on the unit circle corresponding to a given angle.
In the second quadrant, the x-coordinate is negative, and the y-coordinate is positive.
Since the cosine of 3π/4 is positive, we know that COS(3π/4) = √2/2.
Thus, COS[ARCSIN(SIN(3π/4))] = COS[ARCSIN(√2/2)] = COS(3π/4) = √2/2.