SOLUTION: Find the exact value of arcsin(1/8) + arccos(1/8).

Question 1196285: Find the exact value of arcsin(1/8) + arccos(1/8).
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

                D U P L I C A T E ,   T R I P L I C A T E,   Q U A D R U P L I C A T E

I just solved/answered this problem/question.   See the link

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1196146.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1196146.html

///////////////////

If you did not get understanding from my original solution under the referred link,

then I'm afraid nothing will help you.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

A = arcsin(1/8)
B = arccos(1/8)
The goal is to find A+B
As a slight detour, let's find out what sin(A+B) is

Recall from the list of trig identities that
sin(A+B) = sin(A)cos(B)+cos(A)sin(B)

Let's compute each piece
sin(A) = sin(arcsin(1/8))
sin(A) = 1/8
The sine and inverse sine functions cancel each other out.

cos(B) = cos(arccos(1/8))
cos(B) = 1/8
We have similar cancellation going on.

cos(A) = cos(arcsin(1/8))
cos(A) = 3*sqrt(7)/8
See the figure below

I used the pythagorean theorem to determine the 3*sqrt(7) portion

sin(B) = sin(arccos(1/8))
sin(B) = 3*sqrt(7)/8
The steps are similar to the previous section

Now we can put everything together
sin(A+B) = sin(A)cos(B)+cos(A)sin(B)
sin(A+B) = (1/8)*(1/8) + ( 3*sqrt(7)/8 )( 3*sqrt(7)/8 )
sin(A+B) = 1/64 + 63/64
sin(A+B) = (1 + 63)/64
sin(A+B) = 64/64
sin(A+B) = 1
A+B = arcsin(1)
A+B = pi/2
arcsin(1/8) + arccos(1/8) = pi/2

Answer: pi/2 radians (which is equivalent to 90 degrees)

As pointed out by the other tutor, there's nothing particularly special about the 1/8. It turns out that arcsin(x) + arccos(x) = pi/2 for any x on the interval of

RELATED QUESTIONS
1. Use a calculator to find the approximate value of arcsin(0.72). 2. Find the exact... (answered by ikleyn)
Find the exact value of arccos (cos... (answered by lwsshak3)
Find the exact value of arccos... (answered by lwsshak3)
Find the value of... (answered by tommyt3rd)
Find the exact value of each expression. a) cot^-1 (1) and b)... (answered by RAY100)
Find the exact value of the quantity in the interval [0, π]. arccos... (answered by lwsshak3)
hoe to find the exact value of cos(arcsin(-1/2) +... (answered by stanbon,Alan3354)
Find the positive integral solution of equation:... (answered by lynnlo)
find the exact value of each expression. a.) cot^-1(-square root 3) b.)... (answered by stanbon)