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Masteriza [31]
3 years ago
9

Use trigonometric identities to solve each equation within the given domain.

Mathematics
1 answer:
katrin [286]3 years ago
6 0

Recall that the tangent function is defined by

tan(<em>x</em>) = sin(<em>x</em>)/cos(<em>x</em>)

Also recall the double angle identity for sine,

sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)

Then the equation is the same as

3 sin(<em>x</em>)/cos(<em>x</em>) = 4 sin(<em>x</em>) cos(<em>x</em>)

Move everything to one side to prepare to factorize:

3 sin(<em>x</em>)/cos(<em>x</em>) - 4 sin(<em>x</em>) cos(<em>x</em>) = 0

sin(<em>x</em>)/cos(<em>x</em>) (3 - 4 cos²(<em>x</em>)) = 0

As long as cos(<em>x</em>) ≠ 0, we can omit the term in the denominator, so we're left with

sin(<em>x</em>) (3 - 4 cos²(<em>x</em>)) = 0

and so

sin(<em>x</em>) = 0   <u>or</u>   3 - 4 cos²(<em>x</em>) = 0

sin(<em>x</em>) = 0   <u>or</u>   cos²(<em>x</em>) = 3/4

sin(<em>x</em>) = 0   <u>or</u>   cos(<em>x</em>) = ±√3/2

On the interval [0, 2<em>π</em>),

• sin(<em>x</em>) = 0 for <em>x</em> = 0 and <em>x</em> = <em>π</em>

• cos(<em>x</em>) = √3/2 for <em>x</em> = <em>π</em>/6 and <em>x</em> = 11<em>π</em>/6

• cos(<em>x</em>) = -√3/2 for <em>x</em> = 5<em>π</em>/6 and <em>x</em> = 7<em>π</em>/6

(None of these <em>x</em> make cos(<em>x</em>) = 0, so we don't have to omit any extraneous solutions.)

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Jarry is making a strawberry smoothie which measure is greatest the amount of milk cottage cheese or strawberry
Stells [14]

Answer:

Milk

Step-by-step explanation:

The amount of milk, cottage cheese and strawberries used are given in the attached picture.

3/4 cup of milk

2/6 cup cottage cheese

8/12 cup strawberry

Converting the fractions to decimal :

3/4 cup of milk = 0.75

2/6 cup cottage cheese = 0.3333

8/12 cup strawberry = 0.66666

0.75 > 0.6666 > 0.3333

We can conclude that amount of milk is greatest, then strawberry and the least is cottage cheese.

8 0
3 years ago
What is u decreased by 17
blagie [28]
U decreased by 17 is u-17.
if you decrease a number from something, you use subtraction.

therefore, u decreased by 17 is u-17
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3 years ago
Which is greater: 25% of 15 or 15% of 25? Explain your reasoning using algerbreaic representations or visual models
Bingel [31]
25% of 15 is the same as 15% of 25
25%=25/100
25% of 15=(25/100)15=(25*15)/100

15%=15/100
15% of 25=(15/100)25=(25*15)/100

Therefore:
25% of 15=15% of 25
because:
(25/100)15=(15/100)25
(25*15)/100=(25*15)/100
3.75=3.75
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What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Ol
iogann1982 [59]

Answer:

1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.

2. The intrusion of the younger rock by the principle of cross-cutting relationship

3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.

Step-by-step explanation:

In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.

The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.

The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.

6 0
3 years ago
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