Solve y ≥ -2|x

If sin θ = cot θ, then, what is the value of cos θ + 2 cos^2 θ + 2 cos^3 θ + cos^ 4 θ ?

VARVARA [1.3K]

Notice that

cos(θ) + 2 cos²(θ) + 2 cos³(θ) + cos⁴(θ)

= cos(θ) (1 + 2 cos(θ) + 2 cos²(θ) + cos³(θ))

= cos(θ) ([1 + cos(θ)] + [cos(θ) + cos²(θ)] + [cos²(θ) + cos³(θ)])

= cos(θ) ([1 + cos(θ)] + [cos(θ) (1 + cos(θ))] + [cos²(θ) (1 + cos(θ))])

= cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

Given that sin(θ) = cot(θ), by definition of cotangent this tells us that

sin(θ) = cos(θ)/sin(θ) ⇒ cos(θ) = sin²(θ)

and by the Pythagorean identity

cos²(θ) + sin²(θ) = 1

it follows that

cos(θ) = sin²(θ) = 1 - cos²(θ)

Substituting these results into the factorization above gives

cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

= cos(θ) (1 + cos(θ)) (1 + [1 - cos²(θ)] + cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 sin²(θ) (1 + cos(θ))

= 2 (1 - cos²(θ)) (1 + cos(θ))

= 2 (1 + cos(θ) - cos²(θ) - cos³(θ))

= 2 (cos(θ) + cos(θ) - cos³(θ))

= 2 (2 cos(θ) - cos³(θ))

= 2 cos(θ) (2 - cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 (cos(θ) + cos²(θ))

= 2 (1 - cos²(θ) + cos²(θ))

= 2

7 0

3 years ago

The length of the arc of one quadrant is equivalent to theâ _____ of a 90 degrees bend.

Ira Lisetskai [31]

Answer:

Developed Length

Step-by-step explanation:

A developed length is the length along the centre line of a circular shape.

From the question, the degree of bend is 90°

Also, from the question; the length of an arc of 1 quadrant.

1 quadrant = 90°

And the degree of bend = 90° (from the question)

So, it's safe to say 1 quadrant = the degree of bend = 90°

A small change in 90° will move change the quadrant to another quadrant.

So, at exactly 90° (or other multiples of 90° which are 180°, 270° and 360°), it is at its developed length.

8 0

4 years ago

(a) Work out the reciprocal of 1.25

Oxana [17]

Answer:

0.8 OR $\frac{4}{5}$

Step-by-step explanation:

The reciprocal of any number is the number that it multiplies by to equal 1.

The reciprocal can be found by simply converting the number into a fraction and then 'flipping' the fraction as any number multiplied by its reciprocal is 1.

E.g.

No. X/Y * Y/X (its reciprocal) = 1

$\frac{x}{y} *\frac{y}{x} =\frac{xy}{xy} =1$

So, to find the reciprocal of 1.25,we should first convert 1.25 to a fraction.

1.25 = 125/100

$\frac{125/25}{100/25}=\frac{5}{4}$

Now we just flip 5/4 to get our reciprocal:

$\frac{4}{5}$ = 0.8

Test: 0.8 * 1.25 = 1

The reciprocal of 1.25 ( $\frac{5}{4}$ ) is 0.8 ( $\frac{4}{5}$ ).

Hope this helped!

8 0

3 years ago

Cars lose value over time. Every decade, their value decreases by 1/2. A car is bought for $2000. How much is it worth after 1 d

Eva8 [605]

Answer:

The answer is $3000 ok ru understand

3 0

3 years ago

Read 2 more answers

WILL MARK BRAINLIEST!!! EASY QUESTION!!(✿◡‿◡) Can someone please give me an example of a FIFTH DEGREE POLYNOMIAL WITH THREE TERM

saveliy_v [14]

Answer:

f(x) = x⁵ + 3x³ - 2 I think, if its incorrect I apologize

Step-by-step explanation:

6 0

4 years ago

Solve y ≥ -2|x - 1| + 3