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3 years ago

How do I solve these trigonometric equations!!?

1 answer:

3 0

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.

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Help, I don't remember

GenaCL600 [577]

Answer:

x = 144

Step-by-step explanation:

What you need to remember about this geometry is that all of the triangles are similar. As with any similar triangles, that means ratios of corresponding sides are proportional. Here, we can write the ratios of the long leg to the short leg and set them equal to find x.

x/60 = 60/25

Multiply by 60 to find x:

x = (60·60)/25

x = 144

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Comment on this geometry

You may have noticed that the above equation can be written in the form ...

60 = √(25x)

That is, the altitude from the hypotenuse (60) is equal to the geometric mean of the lengths into which it divides the hypotenuse (25 and x).

This same sort of "geometric mean" relation holds for other parts of this geometry, as well. The short leg of the largest triangle (the hypotenuse of the one with legs 25 and 60) is the geometric mean of the short hypotenuse segment (25) and the total hypotenuse (25+x).

And, the long leg of the large triangle (the hypotenuse of the one with legs 60 and x) is the geometric mean of the long hypotenuse segment (x) and the total hypotenuse (25+x).

While it can be a shortcut in some problems to remember these geometric mean relationships, you can always come up with what you need by simply remembering that the triangles are all similar.

3 0

3 years ago

Which equation is an identity?

spayn [35]

7z + 10 - z = 8z - 2(z - 5)
7z + 10 - z = 8z - 2z + 10
6z + 10 = 6z + 10
6z - 6z = 10 - 10
0 = 0

Therefore, 7z + 10 - z = 8z - 2(z - 5)

3 0

3 years ago

Bilal's favorite colors are red and green.

Arte-miy333 [17]

Answer:

P(A∪B) = 1/3

Step-by-step explanation:

Red Garments = 1 red shirt + 1 red hat + 1 red pairs of pants

Total Red Garments = 3

Green Garments = 1 green shirt + 1 green scarf + 1 green pairs of pants

Total Green Garments = 3

The total number of garments = Total Red Garments + Total Green Garments:

3 + 3 = 6

Let A be the event that he selects a green garment

P(A) = Number of required outcomes/Total number of possible outcomes

P(A) = 3/6

Let B be the event that he chooses a scarf

P(B) = 1/6

The objective here is to determine P(A or B) = P(A∪B)

Using the probability set notation theory:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∩B) = Probability that a green pair of pant is chosen = P(A) - P(B)

= 3/6-1/6

= 2/6

P(A∪B) = 1/2 + 1/6 - 2/6

P(A∪B) = 2/6

P(A∪B) = 1/3

8 0

3 years ago

Read 2 more answers

Given that x = 7.7 m and θ = 52°, work out AC rounded to 3 SF.

Helen [10]

Answer:

The answer is 12.5cm

Step-by-step explanation:

cos 52= 7.7/AC

AC= 7.7/ cos 52

AC= 12.5

8 0

3 years ago

Mrs. Larson made 12 pillows from 16 yards of the same fabric how much fabric was used to make each pillow between what two whole

borishaifa [10]

Answer:The answer is given by :

[ The amount of material ] / [The number of pillows made ] = 16 / 12 = 4 /3 = ( 1 + 1/3 ) yds per pillow

So the answer lies between the integers 1 and 2

Step-by-step explanation:

5 0

3 years ago