sin(2arccos(1/4) - arcsin (-1/2))
arccos(1/4) = 1.318116
2arccos(1/4) = 2(1.318116) =
sin(2arccos(1/4) = .4841229
arcsin(-1/2) = -.523599
so
sin(2arccos(1/4) - arcsin (-1/2))
= .4841229 - (-.523599) = 1.00772
thanks
You are welcome.
Actually there is another answer you might consider
since the sine is negative in the 3rd and 4th quadrants (I used the 4th)
arcsin(-1/2) could also have been
pi + .523599 (in the 3rd quadrant)
= 3.66519
and another value at 2pi - .523599
= 5.759587
You will have to decide depending on what domain was given.
thanks again
To find the value of sin(2arccos(1/4) - arcsin(-1/2)), we can break it down step by step:
Step 1: Find the value of arccos(1/4)
Using the inverse cosine function, arccos, we want to find the angle whose cosine is 1/4. We can use a calculator to find this value. If we input arccos(1/4) in radians mode, we get approximately 1.31811 radians.
Step 2: Find the value of arcsin(-1/2)
Using the inverse sine function, arcsin, we want to find the angle whose sine is -1/2. Again, we can use a calculator to find this value. If we input arcsin(-1/2) in radians mode, we get approximately -0.5236 radians.
Step 3: Calculate the expression inside sin()
To find sin(2arccos(1/4) - arcsin(-1/2)), we need to find the value of the expression inside the sin() function.
The expression is 2arccos(1/4) - arcsin(-1/2).
Substituting the values we found in Step 1 and Step 2, we get:
2(1.31811) - (-0.5236)
2.63622 + 0.5236
= 3.15982
Step 4: Calculate sin(3.15982)
Using a calculator, we can calculate sin(3.15982) and find that it's approximately 0.04296.
Therefore, sin(2arccos(1/4) - arcsin(-1/2)) ≈ 0.04296.