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Flauer [41]
2 years ago
14

1. Trig Function

Mathematics
1 answer:
Dima020 [189]2 years ago
4 0

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = <u>tanθ.cosθ</u>

cosθ = <u>sinθ/tanθ</u>

secθ = <u>1/cosθ</u>

cscθ = <u>1/sinθ</u>

tanθ = <u>sinθ/cosθ</u>

cotθ = <u>cosθ/sinθ</u>

<h3>Trigonometric functions </h3>

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

  • sinθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

  • cosθ

From above, we can write that

cosθ = sinθ/tanθ

  • secθ

Secant is the <u>inverse</u> of cosine

∴ secθ = 1/cosθ

  • cscθ (cosecθ)

Cosecant is the <u>inverse</u> of sine

∴ cscθ = 1/sinθ

  • tanθ

tanθ = sinθ/cosθ

  • cotθ

Cotangent is the <u>inverse</u> of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = <u>tanθ.cosθ</u>

cosθ = <u>sinθ/tanθ</u>

secθ = <u>1/cosθ</u>

cscθ = <u>1/sinθ</u>

tanθ = <u>sinθ/cosθ</u>

cotθ = <u>cosθ/sinθ</u>

Learn more on Trigonometric functions here: brainly.com/question/10316891

#SPJ1

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Answer:

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\

It is a homogeneous solution:

y_h(t)=c_1e^{-2i t}+c_2e^{2i t}

Now, we finding a particular solution.

y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\

we get

y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

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A runner finished a total of 1500 kilometers in races before retiring she finished thirty-two 15 kilometer races. The rest of he
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Answer:

The workers will need 10 days to finish the job.

Step-by-step explanation:

To solve this question we can use a compound rule of three. We have:

10 road workers -> 5 days -> 2h/day

2 road workers ->  x days -> 5h/days

The first thing we should do is analyze how the proportions between the variables work, if they're inversely or directly proportional. If we raise the number of workers we expect that the amount of days needed to finish the job lowers and if we raise the number of hours worked in a day we expect that the workers would need less days to finish the job. So we need to invert the fractions that are inversely proportional to the amount of days worked, then we have:

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9. The ticket at right has a perimeter of 42 cm.
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Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.

I've added the image of the ticket as an attachment.

(a) The missing side length

From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.

So, we have:

Perimeter =2\times 11 + 4 \times L

This gives

2\times11 + 4 \times L = 42

22 + 4 \times L = 42

Collect like terms

4 \times L = 42-22

4 \times L = 20

Divide both sides by 4

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(b) The length of the gold lines

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So, the length of the gold line is:

Gold = 4 \times L

Gold = 4 \times 5cm

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(c) The number of gold ink bottles.

n = 200 --- number of tickets

The length of all gold line in the 200 tickets is:

Length = 200 \times Gold

Length = 200 \times 20cm

Length = 4000 cm

Length = 4000 \times 0.01m ---- convert to meters

Length = 40m

Given that:

Bottle = 20m --- 1 bottle for 20 m

The number of bottles (n) is:

n = \frac{Length}{Bottles}

n = \frac{40m}{20m}

n = 2

Hence, 2 bottles of gold ink are enough.

Read more about perimeters at:

brainly.com/question/6465134

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