Use appropriate identities to find exact value cos5pi12 Use

Use appropriate identities to find exact value cos(-5pi/12) = ______________Use a confunction identity to fill in blank sin(25degree) = cos()degree Find the sum? 3pi/3 + pi/5 = ______________

Solution

1) cos( -5*pi/12) = ?

from cos(- theta) = cos(theta)

cos( -5*pi/12) = cos( 5*pi/12)

= cos( 5*180/12)

= cos(75)

= cos( 45+30)

use ( cos (A+B) = cos A*cosB- sinA*sinB)

= cos 45*cos30 - sin 45*sin 30

= ( 1/ 2^1/2)* ( 3^1/2 /2) - ( 1/ 2^1/2)* *(1/2)

cos( -5*pi/12) = 0.2588

2) from cos( 90- theta) = sin (theta)

sin 25 = cos ( 90- 25)

sin 25 = cos 65

3) 3*pi / 3 + pi/5

= 15 pi+ 3 pi / 15

= 18 pi/ 15