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
valentina_108 [34]
2 years ago
6

Find sin theta if cot theta = -2 and cos theta < 0

Mathematics
1 answer:
Katarina [22]2 years ago
6 0

cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>)

So if both cot(<em>θ</em>) and cos(<em>θ</em>) are negative, that means sin(<em>θ</em>) must be positive.

Recall that

cot²(<em>θ</em>) + 1 = csc²(<em>θ</em>) = 1/sin²(<em>θ</em>)

so that

sin²(<em>θ</em>) = 1/(cot²(<em>θ</em>) + 1)

sin(<em>θ</em>) = 1 / √(cot²(<em>θ</em>) + 1)

Plug in cot(<em>θ</em>) = -2 and solve for sin(<em>θ</em>) :

sin(<em>θ</em>) = 1 / √((-2)² + 1)

sin(<em>θ</em>) = 1/√(5)

You might be interested in
What is the probability of rolling an even number with one roll of a number cube?<br>​
oee [108]

Answer:

50% or 1/2

Step-by-step explanation:

There is an even amount of even and odd numbers on a number cube, therefor it is split half and half, giving you 50%.

3 0
2 years ago
An ice skater covered 1500 meters in 106 seconds find the unit rate in meters per second
lukranit [14]

Answer:

14.15m/s

Step-by-step explanation:

\We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 106

(1500 miles ÷ 106) / (106 seconds ÷ 106)

=14.15 miles/ 1 second

=14.15 miles/second

= 14.15 miles per second

6 0
3 years ago
Find the polynomial of minimum degree, with real coefficients, zeros at
drek231 [11]

Answer:

\huge\boxed{p(x)=4x^3-20x^2+4x+300}

Step-by-step explanation:

\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has  a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)

\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300

7 0
3 years ago
In the box, type the number that correctly completes the sentence.
VLD [36.1K]
He would receive $5.63, not including tax
6 0
3 years ago
Find the missing values in each row. Use the percent equation. A: Principal: $100 Interest rate: 5% Time in years: 3 Interest ea
ANEK [815]

Answer:

A.) 15

B.) 1 year

C.) $50

D.) 1.5%

Step-by-step explanation:

The percentage equation goes thus:

Interest earned = principal * rate * time

A)

Principal: $100 Interest rate: 5% Time in years: 3 Interest earned

Interest earned = $100 * 0.05 * 3

Interest earned = $15

B.)

Principa;" $500 Interest rate: 4% Time in years: interest earned: $20

Interest earned = principal * rate * time

20 = 500 * 0.04 * time

20 = 20 * time

Time = 20 / 20 = 1

Time = 1 year

C.)

Principal: Interest rate:10% Time in years: 7 Interest earned:$35

Interest earned = principal * rate * time

$35 = principal * 0.1 * 7

$35 = principal * 0.7

Principal = $35 / 0.7

Principal = $50

D.)

Principal: $200 Interest rate: Time in years:2 Interest earned: $6

Interest earned = principal * rate * time

$6 = $200 * rate * 2

$6 = $400 * rate

Rate = $6/$400

Rate = 0.015 = 1.5%

7 0
3 years ago
Other questions:
  • List the factor pairs of 16
    14·2 answers
  • Simplify the expression.
    11·1 answer
  • Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substi
    6·2 answers
  • 0.003 is 1/10 of???????<br><br><br><br> PLZ HELP ME !
    11·2 answers
  • Find the difference of the complex numbers.
    13·1 answer
  • Use Wolframalpha to find the exact volume of the solid obtained by rotating about x = [pi]/2 the region bounded by y = sin^2x, y
    6·1 answer
  • A regulation-size women's basketball has a diameter of 9.07 inches. What is the surface area of the basketball? Use 3.14 for π a
    7·1 answer
  • 4b + 3 = 2b + 13 Can someone please help me with this problem​
    7·1 answer
  • The table shows data largemouth bass. Use a calculator to find the equation of the line of best fit for the data. Then predict t
    5·1 answer
  • Whats the correct answer answer asap for brainlist
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!