PLEASE HELP!!!!
Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
sin(θ) =
cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =
Answers
cos(theta)=8/17
tan(theta)=-15/8
csc(theta)=-17/15
sec(theta)=17/8
cot(theta)=-8/15
Hope this helps
Answers:
sin(θ) = -15/17 cos(θ) = 8/17 tan(θ) = -15/8 csc(θ) = -17/15 sec(θ) = 17/8 cot(θ) = -8/15=======================================================
Explanation:
Refer to the diagram below. The point (8,-15) is in quadrant 4, which is the southeast quadrant. A right triangle forms where the hypotenuse goes from the origin to the terminal point in question. After applying the pythagorean theorem, the hypotenuse is 17 units long.
Opposite the reference angle θ, greek letter theta, the side is -15. Usually negative lengths are not allowed and don't make any sense; however, I'm making this negative to ensure that sin(θ) ends up negative. This will help with other trig ratios as well.
So,
sin(angle) = opposite/hypotenuse
sin(θ) = -15/17
-----------------
The cosine ratio will involve the adjacent and hypotenuse
cos(angle) = adjacent/hypotenuse
cos(θ) = 8/17
------------------
Tangent is opposite over adjacent
tan(angle) = opposite/adjacent
tan(θ) = -15/8
------------------
The functions csc(θ), sec(θ), and cot(θ) are the functions cosecant, secant, and cotangent in that order.
They represent the reciprocal of sine, cosine, and tangent in that order as well.
Eg: sec(θ) is the reciprocal of cos(θ)
This means,
csc(θ) = -17/15 which is the flip of sin(θ) = -15/17sec(θ) = 17/8 which is the flip of cos(θ) = 8/17cot(θ) = -8/15 which is the flip of tan(θ) = -15/8As an alternative, you could also say
csc(θ) = hypotenuse/opposite = 17/(-15) = -17/15sec(θ) = hypotenuse/adjacent = 17/8cot(θ) = adjacent/opposite = -15/8------------------------
Here's a list of formulas that you can write down on a reference sheet
sin(θ) = y/h cos(θ) = x/h tan(θ) = y/x csc(θ) = h/y sec(θ) = h/x cot(θ) = x/ywhere h is the hypotenuse and h = sqrt(x^2+y^2). Notice that something like tan = y/x is the reciprocal of cot = x/y. The x and y refers to the coordinates of the terminal point given to you. Make sure to reduce all fractions as much as possible. In our case, none of the fractions can be reduced any further.
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Answer:
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Order of Operations: BPEMDAS
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Step 1: Define
Identify
2 × (2 - 6 + 3 + 64 × 3)
Step 2: Evaluate
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Answers
Answer:
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Step-by-step explanation:
This probably isn't the fastest way to solve but....
28,337x1.26%= 357
357x5=1785
28,337+1785=30,122
The 5 came from the # of years the population is increasing
We are required to find the population of Rexburg will be in the year 2022
The population of Rexburg will be in the year 2022 is 30,122 people
Given:
2017 population = 28,337 people
Growth rate per year = 1.26%
let
n = number of years between current and predicted
= 2022 - 2017
n = 5 years
Yearly growth rate = 28,337 × 1.26%
= 28,337 × 0.0126
= 357.0462
Predicted population in 2022 = 2017 population + (357.0462 ×5)
= 28,337 + 1,785.231
= 30,122.231
Approximately, 30,122 people in 2022.
Therefore, the population of Rexburg will be in the year 2022 is 30,122 people
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Which fraction correctly represents 0.63?
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Answers
Answer:
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Step-by-step explanation:
take the numirater and divide by denominator
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Answer:
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Answers
9514 1404 393
Answer:
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Step-by-step explanation:
The equation simplifies to ...
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Answer:
7x - 4x = 21
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Answer:
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Step-by-step explanation:
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Answer:
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y=4(-6)-8= -32
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For the given equation of the line, the complete table is attached below.
Use the concept of the equation of line defined as:
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
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The complete table is attached below.
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Step-by-step explanation:
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Step-by-step explanation:
To build a computer, Tom needs to buy a motherboard for £ 120, and a CPU for
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1 computer = £220
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Kyle is buying a $220 bicycle if the bicycle is on sale for 35% off how much will he save
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Step-by-step explanation:
Okay so first, we know that the bicycle is 220 dollars. So we got to multiply that to the percent. We can't muiltiply it into the percent yet so we turn that percent into 0.35
220 * 0.35
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Answer:
Step-by-step explanation:
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Answer:
y-intercept: [tex](0,-\frac{5}{2} )[/tex]
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Step-by-step explanation:
Hi there!
Important things to note:
the y-intercept occurs when x=0the x-intercept occurs when y=01) Find the y-intercept
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Substitute x with 0
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Divide both sides by -4
[tex]\frac{-4y}{-4} =\frac{10}{-4} \\y=-\frac{5}{2}[/tex]
Therefore, the y-intercept is [tex]-\frac{5}{2}[/tex]. When written in (x,y) form, x will always be 0 while y is the y-intercept:
[tex](0,-\frac{5}{2} )[/tex]
2) Find the x-intercept
[tex]-5x-4y=10[/tex]
Substitute y with 0
[tex]-5x-4(0)=10\\-5x-0=10\\-5x=10[/tex]
Divide both sides by -5
[tex]-5x=10\\\frac{-5x}{-5}= \frac{10}{-5} \\x=-2[/tex]
Therefore, the x-intercept is -2. When written in (x,y) form, x will always be the x-intercept while y is always 0:
[tex](-2,0)[/tex]
I hope this helps!
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Answers
Answer:
y - 5 = 6(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
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Answer:
the axis of symmetry would be: b. x=2
The equation of the axis of symmetry of the parabola will be x = 2. Then the correct option is B.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
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The equation is given below.
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Convert the equation into a vertex form. Then we have
y = 3x² - 12x + 11
y = 3x² - 12x + 12 - 1
y = 3(x² - 4x + 4) - 1
y = 3(x - 2)² - 1
The equation of the axis of symmetry of the parabola is given as,
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