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maksim [4K]
2 years ago
13

Given that cos 63°≈ 0.454, enter the sine of a complementary angle. sin

Mathematics
1 answer:
jek_recluse [69]2 years ago
4 0

Answer:

\cos(63^\circ) is the same as \sin(27^\circ) by co-function identities

Step-by-step explanation:

Remember that complementary angles add up to 90°. The angle that i s complementary to 63° is 27°.

Also recall the co-function identities:

  • sin (90° – x) = cos x
  • cos (90° – x) = sin x

This means that \cos(90^\circ-27^\circ)=\sin(27^\circ)\approx0.454.

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3 0
3 years ago
Find the area of the figure below. Round your answer to one decimal place.
MAVERICK [17]

Answer: 57.1 (rounded)

Step-by-step explanation:

Area of triangle formula: 1/2 x base x height

Area of a semicircle: 1/2 x pi x r^2

(1/2 x 8 x 8) + (1/2 x pi x 4^2)

= 57.1 (rounded)

4 0
2 years ago
In circle P, EG and FH are diameters.<br> What is m EH?
zvonat [6]

Answer:

m(\widehat{EH}) = 130°

Step-by-step explanation:

Angles subtended at the center by the arcs (\widehat{HG}) and (\widehat{EF}) are ∠HPG and  ∠EPF.

Since these angles are the vertical angles both will be equal.

m∠HPG ≅ m∠EPF

3x - 10 = 2x + 10

3x - 2x = 10 + 10

x = 20

Therefore, m(\widehat{HG})=(3\times 20) - 10

                               = 50°

Similarly m(\widehat{EF}) = 50°

In the same way angles subtended at the center will be equal.

m∠EPH ≅ m∠FPG

and m(\widehat{EH})=m(\widehat{FG})

Since m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360°

m(\widehat{EH})+m(\widehat{EH})+50+50=360

2m(\widehat{EH})=360-100

m(\widehat{EH})=130

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3 0
3 years ago
Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a
Bond [772]

f(x)=3\sin x+3\cos x\implies f'(x)=3\cos x-3\sin x

f has critical points where f'=0:

3\cos x-3\sin x=0\implies\cos x=\sin x\implies\tan x=1\implies x=\pm\dfrac\pi4+2n\pi

where n is any integer. We get solutions in the interval \left[0,\frac\pi3\right] for n=0, for which x=\frac\pi4.

At this critical point, we have f\left(\frac\pi4\right)=3\sqrt2\approx4.243.

At the endpoints of the given interval, we have f(0)=3 and f\left(\frac\pi3\right)=\frac{3+3\sqrt3}2\approx4.098.

So we have the extreme values

\max\limits_{x\in\left[0,\frac\pi3\right]}f=3\sqrt2

\min\limits_{x\in\left[0,\frac\pi3\right]}f=3

8 0
3 years ago
The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex
melomori [17]

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

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y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

3 0
3 years ago
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