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
Solve the equation thanks
sashaice [31]
X=-2y+3
Is your answer hope this helps
4 0
3 years ago
Pls help! simple question will give brainliest!
Sphinxa [80]

Answer:

Factor x^{4}−2401

x^{4}−2401

=(x^{2}+49)(x+7)(x−7)

7 0
2 years ago
Read 2 more answers
1) Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for serve
stiv31 [10]

Answer:

a) 0.1 = 10% probability of a tip of $200 or more.

b) 0.4 = 40% probability of a tip of up to $50.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Distribution:

Total of 500 checks.

200 with tips in the interval of 0-20.

100 with tips in the interval of 20-50.

75 with tips in the interval of 50-100.

75 with tips in the interval of 100-200.

50 with tips of 200 or more.

a) What is the probability of a tip of $200 or more?

50 out of 500. So

p = \frac{50}{500} = 0.1

0.1 = 10% probability of a tip of $200 or more.

b) What is the probability of a tip of up to $50?

200 out of 500. So

p = \frac{200}{500} = 0.4

0.4 = 40% probability of a tip of up to $50.

7 0
2 years ago
What is the final cost of a book priced at $10.00 with a tax rate of 5%?
Sophie [7]

Answer:

10.50

Step-by-step explanation:

5% of 10 is 0.5

0.5+10=10.50

5 0
2 years ago
Read 2 more answers
Represent each fraction on the number line <br><br> 0————1
Akimi4 [234]
The answers are 1/5,2/5,3/5,and 4/5
5 0
3 years ago
Other questions:
  • Brian runs 4 miles in 34 minutes. How many minutes per mile does Brian run?
    8·2 answers
  • Pls help me I’ll give brainliest!
    13·2 answers
  • A lead ball weighs 326 grams. Find the radius of the ball to the nearest tenth of a<br> centimeter.
    11·1 answer
  • A __________a0 function forms a line when graphed.
    13·1 answer
  • Which expression is equivalent to<br> 128x8,329 ? Assume y20 and 720
    13·1 answer
  • Filter A is cleaned immediately after it has
    6·1 answer
  • What is the slope of the line that passes through and<br> (-3,-5) and (4,-2)?
    9·1 answer
  • What number, divided by 3/7 , will result in a value of 2 1/3?
    15·1 answer
  • Heeeeeeeellllpppp wiilll ggiivvee bbrraaiinnlliieesstt
    12·2 answers
  • A 16 ounce box of a certain cereal cost $2.24 what is the cost per ounce of the cereal
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!