Question

Help me with my work plz.

Answer 1

Answer:

(√366 - 3)/24

Step-by-step explanation:

Given the following:

cos∝ = √3/8 and sinβ = √3/3

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Get sin∝

Since cos∝ = √3/8

adj = √3

hyp = 8

opp = √8² - (√3)²

opp = √64 - 3

opp = √61

Recall that sin∝ = opp/hyp  

sin∝ = √61/8

Get cosβ

Since sinβ =  √3/3

opp = √3

hyp = 3

adj =√3² - (√3)²

adj = √9-3

adj = √6

Recall that cosβ = adj/hyp

cosβ = √6/3

Substitute the gotten values into the formula

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Sin(∝-β) = ( √61/8)(√6/3)- (√3/8)(√3/3)

Sin(∝-β) = √366/24 - √9/24

Sin(∝-β) = (√366 - 3)/24