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zhannawk [14.2K]
3 years ago
9

How do I solve these trigonometric equations!!?

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0
<span>1) (sin x)(cos x) = 0 This means that either sin x = 0, or cos x = 0. Sin x = 0 when x = 0 or pi. cos x = 0 when x = pi/2 or 3pi/2. 2) cos2x + 2cosx + 1 = 0 First, expand cos2x. Simple trigonometric identity states that cos2x = (cos x)^2 - (sin x)^2.Now, substituting this equation, we get cos2x + 2cosx + 1 = (cos x)^2 - (sin x)^2 + 2cosx + 1. Note that we can now utilize the identity (cos x)^2 = 1 - (sin x)^2 to obtain (cos x)^2 + 2cosx + 1 - (sin x)^2 = 2(cos x)^2 + 2(cos x) = 0. Now, we can see that 2(cos x)^2 + 2(cos x) = 2(cos x)(cos x + 1) = 0. This is true when cos x = 0 or cos x + 1 = 0. Cos x = 0 when x = pi/2 or 3pi/2. cos x = -1 when x = pi. Therefore, x = pi/2, pi or 3pi/2.</span>
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How many times a day do the minute and hour hands form a straight line?
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The picture below shows a box sliding down a ramp:
zimovet [89]

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A = 22 degrees

Step-by-step explanation:

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Vesna [10]

The domain of the function can be represented using set-builder notation as follows: {x | x is a positive integer}. The range of the function can be represented using inequality notation as follows: 0 ≤ y ≤ 100.

<h3>What are the domain and range of the function?</h3>

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

Part A:

Hours Cost

1  10

3  30

11  100

20  100

Part B:

The domain of the function that represents the cost of renting a bicycle is the set of all possible values of the number of hours the bicycle is rented for. In this case, the domain is the set of all positive integers, because the bicycles must be returned the same day they are rented.

The range of the function is the set of all possible values of the cost of renting the bicycle. In this case, the range is the set of all non-negative numbers less than or equal to 100, because the maximum daily fee is $100.

Part C:

The domain of the function can be represented using set-builder notation as follows:

{x | x is a positive integer}

The range of the function can be represented using inequality notation as follows:

0 ≤ y ≤ 100

Learn more about the domain and the range here:

brainly.com/question/21027387

#SPJ1

3 0
1 year ago
Simplify 3a(a^2-3a+4)-4(3a^3-2a^2)
bogdanovich [222]

Answer:

<h2>−9a³ − a² + 12a</h2>

Step-by-step explanation:

3a(a²-3a+4)-4(3a³-2a²) = 3a³ − 9a² + 12a − 12a³ + 8a²

                                     = (3a³ − 12a³) + (− 9a² + 8a²) + 12a  

                                     = −9a³ − a² + 12a

4 0
3 years ago
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