The given expression is:
So, there are two terms in the expression
1)
2) -5
The constant term is -5.
The co-efficient of
is 4.
Given:
Wall 1 & 2 : 26 ft by 9 ft
Wall 3 : 18 ft by 9 ft
Area 1 : 26 ft x 9 ft = 234 ft²
Area 2 : 26 ft x 9 ft = 234 ft²
Area 3 : 18 ft x 9 ft = 162 ft²
Total Area : 234 ft² + 234 ft² + 162 ft² = 630 ft²
1 Gallon = 250 ft²
630 ft² ÷ 250 ft² per gallon = 2.52 gallons
Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
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a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
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b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724
