<h3>
Answer: 33%</h3>
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Explanation:
1/3 converts to the decimal form 0.333333... where the 3's go on forever
5/3 is a similar story but 5/3 = 1.666666.... where the '6's go on forever
The notation 
indicates that the 6's go on forever.
So, 
The horizontal bar tells us which digits repeat. As another example, 
The three dots just mean "keep this pattern going forever".
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Everything mentioned so far has the decimal portions go on forever repeating some pattern over and over.
The only one that doesn't do this is 33% which converts to the decimal form 0.33
The value 0.33 is considered a terminating decimal since "terminate" means "stop". So this is the value that doesn't fit in with the other three items mentioned.
Step-by-step explanation:
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
