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3 years ago

Explain why (cos((theta))? + (sin((theta))2 = 1

Mathematics

1 answer:

frez [133]3 years ago

5 0

Imagine a right triangle where a and b are the legs and c is the hypothenuse.

Pitagora: a²+b²=c²

Divide by c

(a/c)²+(b/c)²=1

But a/c=sin(B) and b/c=cos(B)

Thus sin² + cos² = 1

You might be interested in

Evaluate: ab – bc if a = 4, b = 3, and c = 2

Juli2301 [7.4K]

Answer:

ab-cd

Substitute the values in the equation

(4)(3)-(3)(2)

12-6=6

8 0

3 years ago

Jerry is mowing his lawn .it takes him 1/6 of an hour to mow 3/20 of his years .what portion of the yard does jerry now per hour

Ber [7]

Given that Jerry mows 3/20 yards of lawn in 1/6 hour.

Now we have to found how much Jerry can mow per hour.

We know that "work" and "time" are in direct proportion so we can setup the ratio of work and time to easily find the required work.

$\frac{Portion \; \; of \; \; lawn \; \; mowed}{time}=\frac{\frac{3}{20}}{\frac{1}{6}}$

$\frac{Portion \; \; of \; \; lawn \; \; mowed}{1}=\frac{\frac{3}{20}}{\frac{1}{6}}$

$Portion \; \; of \; \; lawn \; \; mowed=\frac{3}{20}*\frac{6}{1}$

$Portion \; \; of \; \; lawn \; \; mowed=\frac{18}{20}$

$Portion \; \; of \; \; lawn \; \; mowed=\frac{9}{10}$

Hence final answer is $\frac{9}{10}$ yards.

4 0

3 years ago

Read 2 more answers

Use the arc length formula to find the length of the curve y = 2 − x2 , 0 ≤ x ≤ 1. Check your answer by noting that the curve is

Lina20 [59]

By using the arc length formula, we will see that the length of the curve is L = 1.48

<h3>How to use the arc length formula?</h3>

Here we have the curve:

y = 2 - x^2 with 0 ≤ x ≤ 1

And we want to find the length of the curve.

The arc length formula for a curve y in the interval [x₁, x₂] is given by:

$L =\int\limits^{x_2}_{x_1} {\sqrt{1 + \frac{dy}{dx}^2} } } \, dx$

For our curve, we have:

dy/dx = -2x

And the interval is [0, 1]

Replacing that we get:

$L =\int\limits^{1}_{0} {\sqrt{1 + (-2x)^2} } } \, dx\\\\L \int\limits^{1}_{0} {\sqrt{1 + 4x^2} } } \, dx\\$

This integral is not trivial, using a table you can see that this is equal to:

$L = (\frac{Arsinh(2x)}{4} + \frac{x*\sqrt{4x^2 + 1} }{2})$

evaluated from x = 1 to x = 0, when we do that, we will get:

$L = \frac{Arsinh(2) + 2*\sqrt{5} }{4} = 1.48$

That is the length of the curve.

If you want to learn more about curve length, you can read:

brainly.com/question/2005046

8 0

2 years ago

A circle has a radius of 5 meter. What is the length of the arc that is captured by a central angle that measures 120 degrees? R

Irina-Kira [14]

I'd solved the question in attachment. Please watch out the pic..

3 0

3 years ago

Read 2 more answers

How many solutions ?

Volgvan

Answer:

no Solutions

Step-by-step explanation:

-2x -2y = 6

10x + 10y = -30

multiply the first equation by 5 and add the tower equations together

-10x - 10y = 30

+ 10x +10y = -30

you get all zeros so it had no solutions

5 0

3 years ago