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2 years ago

- Use the unit circle to evaluate the six trigonometric functions of theta= 4pi

1 answer:

8 0

<h2> The six trigonometric functions, $\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$ , $\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$ , $\tan \dfrac{\pi}{4} =1$ , $\cot \dfrac{\pi}{4} =1$ , $\sec \dfrac{\pi}{4} =\sqrt{2}$ and $\csc \dfrac{\pi}{4} =\sqrt{2}$ .</h2>

Step-by-step explanation:

We have,

$\dfrac{\pi}{4}$

To write the six trigonometric functions = ?

$\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$

$\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$

$\tan \dfrac{\pi}{4} =1$

$\cot \dfrac{\pi}{4} =1$

$\sec \dfrac{\pi}{4} =\sqrt{2}$

$\csc \dfrac{\pi}{4} =\sqrt{2}$

∴ The six trigonometric functions, $\sin \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$ , $\cos \dfrac{\pi}{4} =\dfrac{1}{\sqrt{2}}$ , $\tan \dfrac{\pi}{4} =1$ , $\cot \dfrac{\pi}{4} =1$ , $\sec \dfrac{\pi}{4} =\sqrt{2}$ and $\csc \dfrac{\pi}{4} =\sqrt{2}$ .

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If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

PLEASEEEEEE HELPPPPPPPPP!!!!!!!!!!!!!!!!! ON ASSESSMENTTTT PRACTICEEEE ITS VERY URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Find the co

adelina 88 [10]

In order to determine the vertex of the given functions, consider that the general form of a quadrati function is:

y = ax² + bx + c

The value of x for the vertex is given by:

x = -b/2a

The value for y, based on the previous values of x, is the y value of the vertex. Use the previous expression to find the vertices:

1. y = x² + 8x - 6

x = -8/2(1) = -4

y(-4) = (-4)² + 8(-4) - 6 = 16 - 32 - 6 = -22

Hence, the vertex is (-4,-22)

2. y = -4x² - 24x - 5

x = -(-24)/2(-4) = -6

y(-6) = -4(-6)² - 24(-6) - 6 = -144 + 144 - 6 = -6

Hence, the vertex is (-6,-6)

3. y = 2x² - 3x + 7

x = -(-3)/2(2) = 3/4 = 0.75

y(3/4) = 2(3/4)² - 3(3/4) + 7 = 18/16 - 9/4 + 7 =5.875

Hence, the vertex is (0.75 , 5.875)

4. y = -x² + 5x - 6

x = -5/2(-1) = 5/2 = 2.5

y(5/2) = -(5/2)² + 5(5/2) - 6 = 0.25

Hence, the vertex is (2.5 , 0.25)

5. y = 1/2 x² + 6x - 5

x = - 6/(2(1/2)) = -6

y(-6) = 1/2 (-6)² + 6(-6) - 5 = -23

Hence, the vertex is (-6 , -23)

6. y = 4x² + 7

x = -0/2(4) = 0

y(0) = 4(0) + 7 = 7

Hence, the vertex is (0 , 7)

8 0

1 year ago

A chestnut falls out of a tree 45 feet above the ground. Use the vertical motion model, H=-16t^2+vt+s s to find how long it take

valentinak56 [21]

Answer:

1.7 seconds

Step-by-step explanation:

we have

$H=-16t^2+vt+s$

where

v is the initial velocity (in feet per second)

s represents the initial height (in feet)

In this problem we have

$v=0$ ---> because the object is dropped

$s=45\ ft$

substitute

$H=-16t^2+45$

Remember that

When the chestnut hit the ground the value of H is equal to zero

For H=0

$-16t^2+45=0$

solve for t

$16t^2=45\\t^2=2.8125\\t=\pm1.7\ sec$

therefore

The solution is t=1.7 sec

7 0

2 years ago

What is a theory in science

alina1380 [7]

A scientific theory is a validated explanation of some aspect of the natural world, based on multiple facts that have been frequently verified through research and experimentation. Fact theories are not "guesses" but reliable accounts of the real world.

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3 years ago

_______ Are numbers that are easy to divide mentally

RSB [31]

Compatible numbers are easy to divide mentally.
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3 years ago

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