1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
siniylev [52]
2 years ago
14

PLEASE HELP!!!!

Mathematics
2 answers:
kherson [118]2 years ago
5 0

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) = -15/17
  • sec(θ) = 17/8 which is the flip of cos(θ) = 8/17
  • cot(θ) = -8/15 which is the flip of tan(θ) = -15/8

As an alternative, you could also say

  • csc(θ) = hypotenuse/opposite = 17/(-15) = -17/15
  • sec(θ) = hypotenuse/adjacent = 17/8
  • cot(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/y

where 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.

algol132 years ago
4 0
Sin(theta)=-15/17
cos(theta)=8/17
tan(theta)=-15/8
csc(theta)=-17/15
sec(theta)=17/8
cot(theta)=-8/15
Hope this helps
You might be interested in
Using the diagram, find sin B. Express your answer as a decimal rounded to the nearest hundredth, such as .86 or 0.86.
inessss [21]
Hi, thank you for posting your question here at Brainly.

This problem could be solved using the Law of Cosines, since we are given with the three sides. The equation goes,

b^2 = a^2 + c^2 - 2accosB. Substituting,

24^2 = 7^2 + 25^2 - 2(7)(25)cosB

Then B = 73.7 degrees. Therefore sinB or sin(73.7) = 0.96.
4 0
2 years ago
A target with a diameter of 14cm has 4 scoring zones by concentric circles. The diameter of the center circle is 2 cm. The width
Leni [432]

Answer:

48.98\%

Step-by-step explanation:

we know that

The probability that it will hit a point in the outer (yellow) ring is equal to divide the area of the yellow ring by the total area of the target

step 1

Find the area of the yellow ring

A=\pi [7^{2} -5^{2}]

A=24\pi\ cm^{2}

step 2

Find the total area of the target

A=\pi [7^{2}]

A=49\pi\ cm^{2}

step 3

Find the probability

24\pi/49\pi=0.4898

Convert to percentage

0.4898*100=48.98\%

4 0
3 years ago
Read 2 more answers
What adds to 10 but also multiplies to -96
klio [65]
X=16
Y=-6

im not good at factorization but this is what i got
8 0
3 years ago
Read 2 more answers
What are two solutions of 3 + 4 |x/2 + 3| = 11?
Alex
3 + 4abs(x/2 + 3) = 11 Subtract 3
4 abs(x/2 + 3) = 11 - 3
4 abs(x/2 + 3) = 8 Divide by 4
abs(x/2 + 3) = 8/4
abs(x/2 + 3) = 2

Solution 1
x/2 + 3 = 2 Subtract 3
x/2 = 2 - 3
x/2 = - 1 Multiply by 2
x/2 *2 = - 2
x = - 2

Solution 2
x/2 + 3 = - 2
x/2 = - 2 - 3
x/2 = - 5 Multiply by 2
x = -5 * 2
x = -10

Solutions
x = - 2 <<<< answer 1
x = -10 <<<< answer 2

3 0
3 years ago
16. Select the equation that has only one solution.
erik [133]

Answer:

A is the answer...........

Explanation

8x+3=3x+8

8x-3x=8-3

5x=5

x=5/5

x=1

8 0
2 years ago
Other questions:
  • 3.2 x (103) is equal to:
    10·2 answers
  • A catering company prepared and served 300 meals at an anniversary celebration last week using eight workers. The week before, s
    5·1 answer
  • Solve this pls!!! I need to turn it into <br>-3<br>_____<br>(x+2)(x-5)​
    10·1 answer
  • conjectures math statement 2(x^2+5)=60 what is the reason? 2x^2+10=60 what is the reason? 2x^2=50 what is the reason? x^2=25 wha
    6·2 answers
  • What is the distance in 6am to 2 am
    14·2 answers
  • 12 grams(g) of a chemical are added to a metal. The amount A, in grams, of the chemical remaining during a reaction with a metal
    8·2 answers
  • Which expressions are equivalent to 2*+7-3652-5)? Check all that apply.
    11·1 answer
  • Convert 7 gallons to cups
    12·2 answers
  • What is the surface area of the rectangular prism below?
    7·1 answer
  • Tell wether x and y show a proportional relationship.<br><br> x 1 2 3 4<br> y 4 8 12 16
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!