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
katovenus [111]
3 years ago
12

Angles α and β are angles in standard position such that: α terminates in Quadrant I and sinα = 3/5 β terminates in Quadrant III

and tanβ = 5/12 . Find sin(α - β).
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
5 0

Answer:

-16/65

Step-by-step explanation:

Given sinα = 3/5 in quadrant 1;

Since  sinα = opp/hyp

opp = 3

hyp = 5

adj^2 = hyp^2 - opp^2

adj^2 = 5^2 = 3^2

adj^2 = 25-9

adj^2 = 16

adj = 4

Since all the trig identity are positive in Quadrant 1, hence;

cosα = adj/hyp = 4/5

Similarly, if tanβ = 5/12 in Quadrant III,

According to trig identity

tan theta = opp/adj

opp = 5

adj = 12

hyp^2 = opp^2+adj^2

hyp^2 = 5^2+12^2

hyp^2 = 25+144

hyp^2 = 169

hyp = 13

Since only tan is positive in Quadrant III, then;

sinβ = -5/13

cosβ = -12/13

Get the required expression;

sin(α - β) = sinαcosβ - cosαsinβ

Substitute the given values

sin(α - β) = 3/5(-12/13) - 4/5(-5/13)

sin(α - β)= -36/65 + 20/65

sin(α - β) = -16/65

Hence the value of sin(α - β) is -16/65

You might be interested in
PLZZZZ HELP WILL MARK BRAINLIEST PLUS 25 POINTS!!!!!!!!!!
Cloud [144]

Answer:

0.6730

Step-by-step explanation:

6 0
3 years ago
Can you answer this step by step? 31,398 ÷ 65 =
Doss [256]

Answer:

483 with a remainder of 3

Step-by-step explanation:

                      4       8       3

                    ---------------------------------

6 5    | 3 1 3 9 8

                       2 6 0

                       ------------------

                              5 3 9  

                               5 2 0

                               ---------------------

                                        1 9 8

                                        1 9 5

                                   ------------------------------

                                                       3

Hope I explain myself :/

5 0
3 years ago
Rearrange the formula to make x the subject.<br><br> y = 4x + 3
allochka39001 [22]

Answer:

x=\frac{y-3}{4}

Step-by-step explanation:

y=4x+3

y-3=4x

\frac{y-3}{4}=x

x=\frac{y-3}{4}

4 0
3 years ago
Read 2 more answers
10.5% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 peo
julia-pushkina [17]

Given:

The sample size n=25

Probability of population is 65 or older is 10.5%.

This date follows the binomial distribution,

\begin{gathered} n=25,p=0.105 \\ X\rightarrow B(n=25,p=0.105) \end{gathered}

To find the probability that at most 2 are 65 or older,

\begin{gathered} P(X=x)=^nC_x(p)^x(1-p)^{n-x} \\ P(0\leq X\leq2)=P(X=0)+P(X=1)+P(X=2) \\ =^{25}C_0(0.105)^0(1-0.105)^{25-0}+^{25}C_1(0.105)^1(1-0.105)^{25-1}+^{25}C_2(0.105)^2(1-0.105)^{25-2} \\ =0.0625+0.1832+0.2579 \\ =0.5036 \\ \approx0.504 \end{gathered}

Answer: Probability is 0.504 .

8 0
1 year ago
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose f
Ludmilka [50]

36 different value meal packages are possible

Step-by-step explanation:

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

4 0
2 years ago
Other questions:
  • Below is the graph of y = g(x)
    12·1 answer
  • Reina and Sam are multiplying (84)5 (73)9. Reina's Work Sam's Work (84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84⋅573⋅9 = 8
    12·1 answer
  • -2xy(3xy^3 – 5xy+ 7y^2)
    12·1 answer
  • Find AB.<br> 69<br> 20<br> 19<br> Is a quizizz
    5·1 answer
  • In the system of equations below, which variable would it be easiest to solve for?
    13·2 answers
  • 1. Solve for x<br> (5x - 10)
    14·2 answers
  • 7t-3t+4t-5t show working​
    14·1 answer
  • What is nine divided by two thirds
    5·2 answers
  • Eugene's grandmother is teaching him how to make her salsa recipe. Each batch of salsa requires 1
    8·1 answer
  • Becky owns a business in an area that has an assessment rate of . The property tax rate is per . What is the effective tax rate?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!