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
sashaice [31]
2 years ago
15

Which expression does sine of the quantity pi plus theta end quantity plus cosine of the quantity pi over 2 minus theta end quan

tity simplify to?
sin θ + cos θ
2cos θ
0
1

(Equation in photo below)

Mathematics
1 answer:
LiRa [457]2 years ago
5 0

Answer:

  (c)  0

Step-by-step explanation:

Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.

__

We can start with the identity ...

  cos(x) = sin(x +π/2)

Substituting the argument of the cosine function in the given expression, we have ...

  cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)

__

The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...

  sin(π +θ) = -sin(θ)

The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...

  cos(π/2 -θ) = -sin(θ -π) = sin(θ)

Then the sum of terms is ...

  sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0

The sum of the two terms is identically zero.

You might be interested in
Can someone help me please?
Delicious77 [7]
I think the mean is 15
3 0
2 years ago
What is 6668 divided by 44
cupoosta [38]
The anwer plus working is 6668/4=151.55
5 0
3 years ago
Is the decimal form of 13/3 a rational number
ludmilkaskok [199]
No Its not Rational Number
8 0
3 years ago
Grandma made an apple pie. Josh and his brother joe finished 4/5 of it. Then 3 friends came over and shared the left over. How m
love history [14]

Answer:

The 3 friends ate 1/5 of the pie.

Step-by-step explanation:

The total of this pie is 5/5 so if Josh and his brother ate 4/5 of the pie that means that there was 1/5 pie left so that is what the 3 friends ate.

Hope I helped :)

4 0
3 years ago
Read 2 more answers
Find the missing numbers.
irinina [24]
Answers

1. 6
2. 1
3. 4
5 0
3 years ago
Read 2 more answers
Other questions:
  • A Machine produces 1000 bowling pins per hour, each valued at $8.37. What is the total value of the pins produce in 1 hour?
    8·2 answers
  • The ratio of miles to hours in activity 1 is 14;2 which can be reduced to 7:1
    12·1 answer
  • What is the coefficient of the second term of the trinomial? (6p + 2)^2 = 36p^2 + _________ p + 4
    8·1 answer
  • Which is the correct simplification of 5.4 x 10^12/ 1.2 x 10^3
    9·1 answer
  • Math.............,,,,,,,,,
    7·2 answers
  • If a point c is inside
    7·2 answers
  • 1.) Subtract unlike fractions using the butterfly method.
    13·1 answer
  • Samyas dog is 1/4 as old as her. In 5 years, her dog will be 1/2 as old as her. Write an equation to represent this situation. H
    15·1 answer
  • Pls Help asap thx alot​
    15·1 answer
  • What is the equation of the line that passes through the points (-4,3) and (2,-6)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!