Without a calculator find the exact value of the following S

Without a calculator find the exact value of the following. Show NO WORK = NO CREDIT. BOX ANSWEF

Solution

i) cos^-1(sin(5*pie/4))

cos^-1( cos( [pie/2]- [ 5*pie/4] ( cos ((pie/2) -@) = sin@)

cos^-1(cos( - 3*pie/4) ( cos(-@) = cos@)

cos^-1(cos( 3*pie/4))

= 3*pie/4

ii) cos( sin^-1(- 3^1/2 /2)) = ? -------------------------------1

let sin^-1(- 3^1/2 /2) = @

sin@ = - 3^1/2 / 2

( sin@ = P / H, P(perpendicular) = -3^1/2 , H = 2 , B ( base) = ( 2² - ( -3^1/2)² )^1/2 = 1)

so from eq 1, cos@ = ?

cos@ = B/H

= 1/2

iii) sin(tan^-1 (-3)) = ? ---------------------------------------A

let tan^-1 (-3) = @

tan@ = -3 = Perpendicular /Base

ie P = -3 , B = 1 , H = 10^1/2

from eq A sin@ = ?

sin@ = P/H

= - 3/ 10^1/2

= -3*10^1/2 / 10