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lara
1 month ago
10

What is the relation between the sine and cosine values of angles in each quadrant? How would you use the 60° angle to find sine

and cosine of 120°, 240°, and 300°? What angles could we find sine and cosine for using information for π/4 and π/6?
Mathematics
1 answer:
Inessa [12.5K]1 month ago
3 0
The sine, cosine, and tangent functions for 60 degrees are equivalent to those for 120, 240, and 300 degrees. Angles of 30 degrees, 45 degrees, and 60 degrees can be paired with corresponding angles from different quadrants. The angles that possess unique sine, cosine, and tangent values are 90, 180, 270, and 360 degrees. The radian measure of π/4 can be calculated using the formula: π/4 * 180/π. The two π values will cancel, leading to: 180/4, which yields the degree measure. This same calculation can also be applied to π/6. Additionally, you can determine radians from degrees by multiplying the degree value by π/180 and then simplifying the fraction or radian as needed. The π will remain in your final result.
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The perimeter of the norwegian flag is 190 inches. What are the dimensions of the flag?
zzz [12365]
<span>The flag's dimensions are 40 inches by 55 inches.

Reasoning<span>:
The perimeter equals the sum of all sides. Being rectangular, opposite sides have equal lengths. Thus, the equation is
y + 11/8 y + y + 11/8 y = 190.

Simplifying, we get
2y + 22/8 y = 190.

Expressing 22/8 as a mixed fraction results in
2y + 2 3/4 y = 190.

Combining terms: 4 3/4 y = 190.

Divide both sides by 4 3/4:
y = 190 ÷ 4 3/4.

Converting 4 3/4 to an improper fraction: y = 190 ÷ 19/4.

Dividing by a fraction means multiplying by its reciprocal:
y = 190 × 4/19 = 760/19 = 40.

Since y = 40, calculate 11/8 y = 11/8 × 40 = 440/8 = 55.</span></span>
8 0
3 months ago
Below are two parallel lines with a third line intersecting them. What is x
PIT_PIT [12445]
136 = x. In detail: When an angle is presented, the angle opposite corresponds to the first equation. The angles at the bottom equal a total of 360, so calculating 46 x 2 = 92. Subtracting 92 from 360 gives 268. Dividing that by 2 yields one of the larger angles as 134 degrees. The upper angle correlates to the lower one, therefore, 136 = x.
8 0
2 months ago
Read 2 more answers
Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
lawyer [12517]

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = \frac{1750}{1000}

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

x = \frac{825,000}{1,000,000}

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

8 0
3 months ago
Would $3.99$ million flies or $47,000,000$ ants have a greater mass? Approximately how much greater, in grams, would the greater
zzz [12365]

Answer:

Ants weigh approximately 118,615,000mg more.

Step-by-step explanation:

Based on a quick search, the average housefly weighs around 11.5mg, while an ant averages at 3.5mg. With these average weights, we can calculate the total weight of each species.

Flies: 3,990,000 * 11.5mg = 45,885,000mg

Ants: 47,000,000 * 3.5mg = 164,500,000mg

Consequently, it's clear that the 47 million ants possess a greater mass, specifically

164,500,000 - 45,885,000 = 118,615,000mg more

3 0
1 month ago
Brianna's teacher asks her which of these three expressions are equivalent to each other. Expression A: 9x - 3x - 4 Expression B
PIT_PIT [12445]

Answer: Expressions A and C yield the same result.

Step-by-step explanation:

When simplifying, it turns out that only A and C reduce to 6x-4

3 0
1 month ago
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