A car is driving at the speed of 58 km/h.How much time will it take to drive for distance 32 miles?
Complete each statement regarding an angle θ and its reference angle theta hat using radian measure. (Assume 0 ≤ θ < 2π. Give your answers in terms of θ.) (a) If θ is in QI, then theta hat = . (b) If θ is in QII, then theta hat = . (c) If θ is in QIII, then theta hat = . (d) If θ is in QIV, then theta hat = .
The reference angle is simply the acute angle between the terminal side and the x-axis
The terminal angles in the four quadrants are
[tex]\bar \theta = \theta[/tex].[tex]\bar \theta = \pi - \theta[/tex].[tex]\bar \theta = \theta - \pi[/tex].[tex]\bar \theta = 2\pi - \theta[/tex]The given parameters are:
[tex]\theta \to[/tex] reference angle
[tex]\bar \theta \to[/tex] terminal angle
(a) If the reference angle is in the first quadrant
In the first quadrant, the x-axis is at [tex]0\ rad[/tex]
So, the terminal angle is:
[tex]\bar \theta = \theta - 0[/tex]
[tex]\bar \theta = \theta[/tex]
(b) If the reference angle is in the second quadrant
In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],
While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis
So, the terminal angle is:
[tex]\bar \theta = \pi - \theta[/tex]
(c) If the reference angle is in the third quadrant
Here, the x-axis is still at [tex]\pi \ rad[/tex],
But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]
It means that, we have to subtract the x-axis from the reference angle.
So, the terminal angle is:
[tex]\bar \theta = \theta - \pi[/tex]
(d) If the reference angle is in the fourth quadrant
Here, the x-axis is at [tex]2\pi \ rad[/tex]
And the reference angle is between [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis.
So, the terminal angle is:
[tex]\bar \theta = 2\pi - \theta[/tex]
See attachment for illustration of terminal angles
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Final answer:
When dealing with angles in radians and their reference angles, each quadrant has a specific relationship for determining the reference angle based on the given angle θ.
Explanation:
Radian Measure with Reference Angles:
If θ is in QI, then θ hat = θ
If θ is in QII, then θ hat = π - θ
If θ is in QIII, then θ hat = θ - π
If θ is in QIV, then θ hat = 2π - θ
family drinks 1 3/4 gallons of milk every 4 1/2 days what is the unit rate of milk per day
How many terms are in the arithmetic sequence 7, 0, −7, . . . , −175?
Michael sold his house for $548,900, which was 160% of the amount he paid for it. Calculate the amount he paid for the property.
a woman walks in and steals 100 from a register. 5 minutes later uses the same 100 to buy merchandise from that same store and buys 70 worth of merchandise with that same 100. he gives her 30 in change. how much did the store lose
What relationship do the ratios of Sin X and Cos y share ?
The ratios of sin (x) and cos (y) are both identical [tex](\frac{6}{10}\; and\; \frac{6}{10})[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. A math tool applied for finding angles or sides in a right triangle is trigonometric ratios.
The main trigonometric ratios are:
[tex]sin(\alpha )=\frac{opposite\;side}{hypotenuse} \\ \\ cos(\alpha )=\frac{adjacent\;side}{hypotenuse}\\ \\ tan(\alpha )=\frac{sin (\alpha )}{cos(\alpha } =\frac{opposite\;side}{adjacent\;side}[/tex]
The question asks the sin x and cos y, for solving this you should apply the trigonometric ratios. Therefore,
[tex]sin (x)=\frac{opposite\; side}{hypotenuse} =\frac{6}{10}[/tex]
and
[tex]cos (y)=\frac{adjacent\; side}{hypotenuse} =\frac{6}{10}[/tex]
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A driveway is 40 yards long. About how many meters long is it? Round to the nearest hundredth
What is 129,543 rounded to the nearest ten thousand
Reina and Sam are multiplying (84)5 (73)9. Reina's Work Sam's Work (84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84⋅573⋅9 = 820727 Is either of them correct? Explain your reasoning.
a large bag of cashews weighs 8 1/3 pounds one serving is 1/3 pound how many servings are in the bag
What is the product in simplest form?
−89⋅56
The answer in siplest form is -
Two right triangles are congruent. Find the value of x.
right triangle with angle of 33 degrees, right triangle with angle of 9 x minus 15 degrees
Select one:
a. 5
b. 6
c. 8
d. 12
Find the ratio and simplify. In this triangle, find the ratio of the shortest side to the longest. A triangle has three sides with lengths 15.2, 5.6, 14.1
What percent is 6 out of 30? 2% 6% 20% 30%
Algebra help me please ILL MARK BRAINIEST
Solve the absolute value equation. |x| = –45
F=J+Jrt solve following formula for t
To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.
Explanation:This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.
Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.
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A scuba diver swimming at the Deppe shown, and then swim 0.5 feet toward the surface every three seconds. What is the location of the scuba diver, relative to the surface, after 15 seconds?
What is the simplified expression for the expression below? 1/2(8x+4)+1/3(9-3x)
Answer:
3x + 5
Step-by-step explanation:
anyone help me please!
A stereo listed for $350 is on sale for 20% off the list price. The sales tax is 6%. What total price does a customer pay for the stereo if she/he buys it on sale?
1 $324.00
2 $259.00
3 $262.20
4 $296.80
5 $301.00
"example 1: the radius of a circle is 3 inches. what is the area?"
A section of a roller coaster track forms a parallelogram ABCD. If m∠ABC = 72°, what is m∠DAB? A) 72° B) 108° C) 144° D) 216°
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
A section of a roller coaster track forms a parallelogram ABCD.
If m∠ABC = 72°
We need to find the m∠DAB,
Since ABCD is a parallelogram .
So, "Sum of interior angles on the same side is supplementary":
[tex]m\angle ABC+m\angle DAB=180\textdegree\\\\72\textdegree+m\angle DAB=180\textdegree\\\\m\angle DAB=180\textdegree-72\textdegree\\\\m\angle DAB=108\textdegree[/tex]
Hence, Option 'B' is correct.
How much greater is the area of a square with a side length of 9 inches than the area of a circle with a radius of 3 inches?
45+5/6x=50
need to find x and math for x
The solution of expression is, x = 6
We have to give that,
An expression to simplify as,
⇒ 45 + 5/6x = 50
Now, Simplify the expression by combining like terms,
⇒ 45 + 5/6x = 50
Subtract 45 on both sides,
⇒ 45 + 5/6x - 45 = 50 - 45
⇒ 5/6x = 5
Multiply by 6 on both sides,
⇒ 5x = 5 × 6
⇒ 5x = 30
Divide by 5 on both sides,
⇒ x = 30/5
⇒ x = 6
So, The solution is, x = 6
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What value of x makes the equation below true?
6x - 9 = 39
A. 13
B. 5
C. 8
D. 24
Jenny drove 1,255 miles last week. She drove 187 miles on Monday. On Tuesday, she drove 53 more miles than on Monday, on Wednesday she dove 26 more miles than on Tuesday. How many more miles did Jenny drove on Monday and tuesday together than on Wednesday and Thursday together?
[tex] \frac{dx}{dt} = \frac{t^{2}+3tx+ x^{2} }{ t^{2} } [/tex]
Caroline bought 20 shares of stock at 10 ½, and after 10 months the value of the stocks was 11 ¼. If Caroline were to sell all her shares of this stock, how much profit would she make? A. $210 B. $10 C. $15 D. $225
Outlet malls sell goods _____
1. at a discount
2. add all the items together at their sales cost then add salves tax
3. $26.75
4. $66.23