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KATRIN_1 [288]
3 years ago
8

Sin\theta +cos\theta =1

Mathematics
1 answer:
Mamont248 [21]3 years ago
4 0

Answer:

θ = 2 π n_1 + π/2 for n_1 element Z  or θ = 2 π n_2 for n_2 element Z

Step-by-step explanation:

Solve for θ:

cos(θ) + sin(θ) = 1

cos(θ) + sin(θ) = sqrt(2) (cos(θ)/sqrt(2) + sin(θ)/sqrt(2)) = sqrt(2) (sin(π/4) cos(θ) + cos(π/4) sin(θ)) = sqrt(2) sin(θ + π/4):

sqrt(2) sin(θ + π/4) = 1

Divide both sides by sqrt(2):

sin(θ + π/4) = 1/sqrt(2)

Take the inverse sine of both sides:

θ + π/4 = 2 π n_1 + (3 π)/4 for n_1 element Z

or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z

Subtract π/4 from both sides:

θ = 2 π n_1 + π/2 for n_1 element Z

or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z

Subtract π/4 from both sides:

Answer: θ = 2 π n_1 + π/2 for n_1 element Z

or θ = 2 π n_2 for n_2 element Z

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A toy company makes rectangular sandboxes that measure 6 feet by 5 feet by 1.2 feet. A customer buys a sandbox and 40 cubic feet
Iteru [2.4K]

Answer:

Customer has bought too much sand

Step-by-step explanation:

Given that the dimensions (Length, Width and Height) of rectangular box are = 6,5, 1.2.

Volume of a rectangular box = Length * Width * Height

=> 6*5*1.2

=> 36 cubic feet

As mentioned, customer bought a sand box and <u>40 cubic feet of sand.</u>

So,

Volume of rectangular box (R) = 36 cubic feet

Volume of Sand (S) = 40 cubic feet

From analysis

S > R

Which shows that the capacity of sandbox is 36 cubic feet and volume is 40 feet that is a little greater than desired capacity.

Therefore, customer has bought too much sand.

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3 years ago
PLEASE HELP ME ASAP?!?
Blababa [14]

Answer:

f(x) = \frac{1}{4}x^{2}  > f(x) = -0.5x² > f(x) = x²

Step-by-step explanation:

In a quadratic function leading coefficient decides the width of a graph.

In simpler words, leading coefficient decides the vertical stretch of the graph.

Higher the value of leading coefficient, higher the vertical stretch.

When a graph is vertically stretched it becomes narrower.

(Note: Minus sign of the coefficient decides the opening of the graph, upwards or downwards)

Therefore, f(x) = x² having coefficient = 1 is the narrowest and f(x) = \frac{1}{4}x^{2} will be the widest.

So the descending order will be,

f(x) = \frac{1}{4}x^{2}  > f(x) = -0.5x² > f(x) = x²

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3 years ago
What unit of measurement would you use to measure the distance from your home to the grocery store?
Ksivusya [100]

Answer:

the answer is kilometer.

Step-by-step explanation:

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Step-by-step explanation:

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Emilio is decorating a ballroom ceiling with a garland the width of the rectangle ceiling is 9 m in a diagonal distance from La
Gnesinka [82]

Answer:

Emilio will need 42 metres length of garland to decorate the length of the ceiling.

Step-by-step explanation:

Step 1: Determining the length of the ceiling

The Width of ceiling = 9 m

The Diagonal of ceiling = 15 m

The Length of the ceiling = y m

The width, diagonal and length of the ceiling forms a right-angle triangle with the diagonal as the hypotenuse

From Pythagoras theorem: 15² m² = 9² m² + y²

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Take square root of both sides

y = 12 m

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Step 2: Determining the perimeter of the ceiling

Perimeter of the ceiling = 2 ( length + width)

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Therefore, Emilio will need 42 metres length of garland to decorate the length of the ceiling.

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