Question

Trigonometry

Special Right Triangles
Find the exact value of cosec 60* + sec 30* + sin 60*.

Answer 1

= 3.175

Explanation:

`\csc( \alpha ) = (1)/( \sin( \alpha ) ) \\ \sec( \alpha ) = (1)/( \cos( \alpha ) ) \\ \\ \\ \csc(60) + \sec(30) + \sin(60) \\ = (1)/( \sin(60) ) + (1)/( \cos(30) ) + \sin(60) \\ = (1)/( ( √(3) )/(2) ) + (1)/( ( √(3) )/(2) ) + ( √(3) )/(2) \\ = (2)/( √(3) ) + (2)/( √(3) ) + ( √(3) )/(2) \\ = (4)/( √(3) ) + ( √(3) )/(2) \\ = (2(4) + ( √(3) ) √(3) )/(2 √(3) ) \\ = (8 + 3)/(2 √(3) ) \\ = (11)/(2 √(3) ) \\ = (11)/(2 √(3) ) * (2 √(3) )/(2 √(3) ) \\ = (22 √(3) )/(4( √(3) )^(2) ) \\ = (22 √(3) )/(4(3)) \\ = (22 √(3) )/(12) \\ = (11 √(3) )/(6) \\ = 3.175`

Answer 2

11sqrt(3)/6

Explanation:

sin(60) = sqrt(3)/2

cosec(60) = 2/sqrt(3) = 2sqrt(3)/3

cos(30) = sqrt(3)/2

sec(30) = 2sqrt(3)/3

2sqrt(3)/3 + 2sqrt(3)/3 + sqrt(3)/2

Lcm: 6

sqrt(3)(4+4+3)/6

11sqrt(3)/6