Find the value of tan(1/2sin^-1 15/17)
and
sin[pi/2-cos(1/2)]
Thanks.
arcsin 15/17 suggests a 8-15-17 right triangle. The angle is 61.93 degrees. half of that is 30.96 degrees. The tangent of that is 0.600
There is a formula that says that tan (x/2) = sin x/(1 + cos x)
You can use that to write
tan [(1/2)sin^-1(15/17)] = (15/17)/[1 + 8/17)] = 15/25 = 3/5
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In the second problem, did you mean to write cos(1/2) or cos^-1(1/2) ? In the former case, use the formula for
cos(x - y)
To find the value of tan(1/2sin^(-1)(15/17)), we can follow these steps:
Step 1: Use the inverse sine function to find the angle whose sine is (15/17).
sin^(-1)(15/17) ≈ 0.8901 radians.
Step 2: Divide the angle found in step 1 by 2.
(1/2) * 0.8901 ≈ 0.4451 radians.
Step 3: Use the tangent function to find the value of tan(0.4451).
tan(0.4451) ≈ 0.4923.
Therefore, the value of tan(1/2sin^(-1)(15/17)) is approximately 0.4923.
Now, let's move on to the second part:
To find the value of sin[π/2-cos(1/2)], we can follow these steps:
Step 1: Evaluate cos(1/2).
cos(1/2) ≈ 0.8776.
Step 2: Calculate π/2 - cos(1/2).
π/2 - cos(1/2) ≈ π/2 - 0.8776 ≈ 0.6947 radians.
Step 3: Use the sine function to find the value of sin(0.6947).
sin(0.6947) ≈ 0.6410.
Therefore, the value of sin[π/2-cos(1/2)] is approximately 0.6410.