Question

if alpha + beta = π by 2 and sin alpha = 1 by 3 then find out sin beta

Answer 1

$good \: \: \: morning \: \\ \\ \\ \\ sin( \alpha ) = \sin((\pi \div 2) - \beta ) \\ \\ \\ \\ \cos( \beta ) = 1 \div 3 \\ \\ \\ \\ \\ \sin( \beta ) = \sqrt{(1 - \cos {}^{2} ( \beta ) } \\ \\ \sin( \beta ) = \sqrt{(9 - 1) \div 9} \\ \\ \\ \\ \\ \sin( \beta ) = 2 \sqrt{2} \div 3$

Answer 2

Answer:

Step-by-step explanation:

since a + b = π/2

a and b are complimentary angles

thus sin b = cos a

we know sin a = 1/3

make a sketch of your right-angled triangle, find the adjacent side to be √8

thus cos a = √8/3

so sin b = √8/3 or 2√2/3