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
<span>I have been a high school/jr high math teacher for the past 13 years. I am happy to explain how to proceed with this problem.
A square is a figure where ALL sides are exactly the same. The find the area of the square you would multiply one side times another side. You would be multiplying a number times itself. So if you already have the area, you would take the square root to find your answer. When you do, you end up with 21.21 square inches rounded to the nearest hundredth.</span>
Answer:
32, 45
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
The LCM is 18.
9x2=18
2x9=18
Solution for (-4z^2-11u)-5z^2=
<span>Simplifying
(-4z2 + -11u) + -5z2 = 0
Reorder the terms:
(-11u + -4z2) + -5z2 = 0
Remove parenthesis around (-11u + -4z2)
-11u + -4z2 + -5z2 = 0
Combine like terms: -4z2 + -5z2 = -9z2
-11u + -9z2 = 0
Solving
-11u + -9z2 = 0
Solving for variable 'u'.
Add '9z2' to each side of the equation.
-11u + -9z2 + 9z2 = 0 + 9z2
Combine like terms: -9z2 + 9z2 = 0
-11u + 0 = 0 + 9z2
-11u = 0 + 9z2
Remove the zero:
-11u = 9z2
Divide each side by '-11'.
u = -0.8181818182z2
Simplifying
u = -0.8181818182z<span>2</span></span>