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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Answers
Answer:
Step-by-step explanation:
3/5x+30=150
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x∈R
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Step-by-step explanation:
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Answer:
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Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
2 × (2 - 6 + 3 + 64 × 3)
Step 2: Evaluate
(Parenthesis) Multiply: 2 × (2 - 6 + 3 + 192)(Parenthesis) Subtract: 2 × (-4 + 3 + 192)(Parenthesis) Add: 2 × (-1 + 192)(Parenthesis) Add: 2 × 191Multiply: 382Please answer this question
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Answer:
Step-by-step explanation:
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Answer:
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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
[tex]-5x-4y=10[/tex]
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[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]
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I hope this helps!
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Step-by-step explanation:
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Answers
9514 1404 393
Answer:
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Step-by-step explanation:
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Taking antilogs, the equation becomes ...
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Step-by-step explanation:
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the 3rd box
Step-by-step explanation:
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Answers
Answer:
30,122
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We are required to find the population of Rexburg will be in the year 2022
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Answer:
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from above we have:
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and
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Answers
Answer:
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Step-by-step explanation:
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Answer:
$143
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35% = 0.35
220 * 0.35 = 77 = discount
Now you want to see how much it will be when the discount is applied
220-77 = 143
The bicycle is $143 when discount is applied, you save $77
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9514 1404 393
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Clearly, the probability of drawing a heart out of the deck is 13/52, or 1/4. The probability of drawing an even number as card #2 (∈{2,4,6,8,10}) for any suit is 20/51, except when the first card drawn is an even heart, then the probability of the second draw is 19/51.
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