Determine the angle a for arcsina arcos12 piSolutionWell r

Determine the angle a for arcsina + arcos1/2 = pi.

Solution

We\'ll re-write arccos (1/2) = pi/3

We\'ll re-write the equation:

arcsina + pi/3 = pi

We\'ll subtract pi/3 both sides:

arcsin a = pi - pi/3

arcsin a = (3pi-pi)/3

arcsin a = 2pi/3

We\'ll take the function sine both side.

sin(arcsin a) = sin 2pi/3

According to the rule, sin(arcsin a) = a. Based on the rule, we\'ll have sin(arcsin a) = a.

a = sin 2(pi/3)

sin 2(pi/3) = 2sin(pi/3)*cos(pi/3)

sin pi/3 = sqrt3/2

cos pi/3 = 1/2

We\'ll substitute the values of the functions sine and cosine in the formula 2sin(pi/3)*cos(pi/3) and we\'ll get:

sin 2(pi/3) = 2sqrt3/2*2

We\'ll simplify and we\'ll get:

sin 2(pi/3) = sqrt3/2

So, a = sqrt3/2.