1Find the exact value of the expression secsin12129 2When th

1-Find the exact value of the expression. sec(sin^1(21/29))

2-When the moon is exactly half full, the earth, moon, and sun form a right angle (see the figure). At that time the angle formed by the sun, earth, and moon (using the earth as its vertex) is measured to be 89.85°. If the distance from the earth to the moon is 240,000 mi, estimate the distance from the earth to the sun. (Round your answer to one decimal place.)

Solution

1)  sec(sin^1(21/29))

let y = sin^-1(21/29)

siny = 21/29

cosy = 20/29----> secy = 29/20

y = sec^-1(29/20)

So, sec(sin^1(21/29)) = secy = secsec^-1(29/20) = 29/20