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
GalinKa [24]
3 years ago
6

Cosθ=−2√3 , where π≤θ≤3π2 .

Mathematics
1 answer:
Alex787 [66]3 years ago
8 0

Answer:

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

Step-by-step explanation:

step 1

Find the  sin(\theta)

we know that

Applying the trigonometric identity

sin^2(\theta)+ cos^2(\theta)=1

we have

cos(\theta)=-\frac{\sqrt{2}}{3}

substitute

sin^2(\theta)+ (-\frac{\sqrt{2}}{3})^2=1

sin^2(\theta)+ \frac{2}{9}=1

sin^2(\theta)=1- \frac{2}{9}

sin^2(\theta)= \frac{7}{9}

sin(\theta)=\pm\frac{\sqrt{7}}{3}

Remember that

π≤θ≤3π/2

so

Angle θ belong to the III Quadrant

That means ----> The sin(θ) is negative

sin(\theta)=-\frac{\sqrt{7}}{3}

step 2

Find the sec(β)

Applying the trigonometric identity

tan^2(\beta)+1= sec^2(\beta)

we have

tan(\beta)=\frac{4}{3}

substitute

(\frac{4}{3})^2+1= sec^2(\beta)

\frac{16}{9}+1= sec^2(\beta)

sec^2(\beta)=\frac{25}{9}

sec(\beta)=\pm\frac{5}{3}

we know

0≤β≤π/2 ----> II Quadrant

so

sec(β), sin(β) and cos(β) are positive

sec(\beta)=\frac{5}{3}

Remember that

sec(\beta)=\frac{1}{cos(\beta)}

therefore

cos(\beta)=\frac{3}{5}

step 3

Find the sin(β)

we know that

tan(\beta)=\frac{sin(\beta)}{cos(\beta)}

we have

tan(\beta)=\frac{4}{3}

cos(\beta)=\frac{3}{5}

substitute

(4/3)=\frac{sin(\beta)}{(3/5)}

therefore

sin(\beta)=\frac{4}{5}

step 4

Find sin(θ+β)

we know that

sin(A + B) = sin A cos B + cos A sin B

so

In this problem

sin(\theta + \beta) = sin(\theta)cos(\beta)+ cos(\theta)sin (\beta)

we have

sin(\theta)=-\frac{\sqrt{7}}{3}

cos(\theta)=-\frac{\sqrt{2}}{3}

sin(\beta)=\frac{4}{5}

cos(\beta)=\frac{3}{5}

substitute the given values in the formula

sin(\theta + \beta) = (-\frac{\sqrt{7}}{3})(\frac{3}{5})+ (-\frac{\sqrt{2}}{3})(\frac{4}{5})

sin(\theta + \beta) = (-3\frac{\sqrt{7}}{15})+ (-4\frac{\sqrt{2}}{15})

sin(\theta + \beta) = -\frac{\sqrt{7}}{5}-4\frac{\sqrt{2}}{15}

You might be interested in
Anybody Know This. ?
Ganezh [65]

Answer:

scalene acute

Step-by-step explanation:

6 0
2 years ago
Add the following 2 wholes and 3/8 plus 3 wholes and 3/7
FinnZ [79.3K]

Answer:

325/56

is the answer

6 0
3 years ago
Read 2 more answers
Plz answer asap I rlly need help​
Alex17521 [72]

Answer:

-8/10, -3/16, 3/16

Step-by-step explanation:

5 0
3 years ago
A 24.6 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 12.3 g marble moving in the same dir
Softa [21]

Answer:

Velocity of the 24.6 g marble is 31 cm/s.

Step-by-step explanation:

Given:

Marble 1:

Mass of the marble (m_1) = 12.3 gm

Velocity of m_1 before collision v_1_i = 15.5 cm/s

Velocity of m_1 after collision v_1_f = 77.5 cm/s

Marble 2:

Mass of the marble (m_2) = 24.6 gm

Velocity of m_2 before collision v_2_i = 62 cm/s

Velocity of m_2 after collision v_2_f = ?

From the law of conservation of momentum, we know that momentum before equals the momentum after :

So,

⇒ P(i)=P(f)

⇒ (m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)

⇒ Plugging the values.

⇒ (12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)

⇒ 190.65+1525.2=953.25+24.6\times v_2_f

⇒ 1715.85=953.25+24.6\times v_2_f

⇒ 1715.85-953.25=24.6\times v_2_f ...subtracting both sides 953.25

⇒ 762.6=24.6\times v_2_f

⇒ \frac{762.6}{24.6}\ =v_2_f ...dividing both sides with 24.6

⇒ 31=v_2_f

⇒ v_2_f =31 cm/s

The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.

6 0
3 years ago
before his shopping spree, Elmer owned 52 scooters. Then he bought 82 more scooters. what is the ratio of scooters purchased to
laiz [17]

Answer:

Step-by-step explanation:

82 / (52+82)

82 / 134

41 / 67  

6 0
2 years ago
Other questions:
  • Ben Roethlisberger was on the 45 yd. line. He got sacked and pushed back 7 yards. Which integer represents the yard line he is o
    15·1 answer
  • Triangle ABC is shown below: Triangle ABC is shown. A is at 2, 1. B is at negative 1, 4. C is at 3, 7. If triangle ABC is reflec
    6·2 answers
  • 2 liters of orange juice and 1.5 liters of applejuice
    11·1 answer
  • A bicyclist travels at a constant speed of 18 miles per hour for a total of 27minutes. Choose the function, the domain and the r
    11·1 answer
  • PLS HELP Will give brainliest
    14·1 answer
  • What is the circumference of the circle? (C = πd or C = 2πr) Use 3.14 for π
    14·2 answers
  • What is the area of this? please help me ! screen shot of assignment attached
    9·1 answer
  • Which algebraic expression represents “the class was divided into four equal groups”?
    10·2 answers
  • Solve the proportion ASAP help do both questions
    8·1 answer
  • Will the point of the arrow in Figure Bhave the same angle measure as the point of the arrow in Figure A? Explain your answer.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!