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
ch4aika [34]
3 years ago
12

Rewrite each expression in terms of sine and cosine only.

Mathematics
1 answer:
Sliva [168]3 years ago
6 0

Answer:

1. Cosθ / SineθCosθ

2. Sineθ / Cos²θSineθ

3. Cosθ / Sineθ

4. Cos²θ + Sin²θ – Sin²θ

Step-by-step explanation:

1. SecθCotθ

Recall

Sec θ = 1/Cos θ

Cot θ = 1/Tan θ

But Tan θ = Sine θ / Cos θ

Thus,

Cot θ = 1 ÷ Sine θ / Cos θ

Cot θ = 1 × Cos θ / Sine θ

Cot θ = Cos θ / Sine θ

Therefore,

SecθCotθ = 1/Cos θ × Cos θ / Sine θ

SecθCotθ = Cosθ / SineθCosθ

2. SecθTanθCscθ

Recall

Sec θ = 1/Cos θ

Tan θ = Sine θ / Cos θ

Csc θ = 1/Sine θ

Thus,

SecθTanθCscθ =

1/Cosθ × Sineθ/Cosθ × 1/Sineθ

= Sineθ / Cos²θSineθ

3. Cscθ/Secθ

Recall

Csc θ = 1/Sine θ

Sec θ = 1/Cos θ

Thus,

Cscθ/Secθ = 1/Sine θ ÷ 1/Cos θ

= 1/Sine θ × Cos θ

= Cosθ / Sineθ

4. Cosθ / Secθ

Recall

Sec θ = 1/Cos θ

Cosθ / Secθ = Cosθ ÷ 1/Cosθ

= Cosθ × Cosθ

= Cos²θ

Recall

Cos²θ + Sin²θ = 1

Cos²θ = 1 – Sin²θ

But

1 = Cos²θ + Sin²θ

Thus,

Cos²θ = Cos²θ + Sin²θ – Sin²θ

Therefore,

Cosθ / Secθ = Cos²θ + Sin²θ – Sin²θ

You might be interested in
Zack, Jack and Sasha earned £250 altogether delivering leaflets.
AleksAgata [21]

Answer:

Zack earned £125, Jack earned £75, and Sasha earned £50

Step-by-step explanation:

Considering the number of leaflets delivered

Zack 50%, Jack 30% and Sasha 20%

Total delivered = 50 + 30 + 20 = 100%

If they earn £250 on the 100% delivery, then each will have as shown below

Zack = (50/100)*250

= 5*25

= £125

Jack = (30/100)*250

= 3*25

= £75

Sasha = (20/100)*250

=2*25

= £50

5 0
3 years ago
Read 2 more answers
Rahul earns 21,000 in 7 months.
tekilochka [14]

Answer:

a _ 12×21000/7 = 36000

b _ 33 × 7 / 21000= 11 months

8 0
2 years ago
Can you help me with try these B?
Softa [21]
A. expanded, you get XxXxXxXxXxXxXxX over XxXxXxXxX
 b.XxXxX or X³
c. I would just cancel out the 5 Xs on the top line against the 5 Xs on the bottom, leaving X³.
6 0
3 years ago
Find the length of the arch
posledela
Use the formula....central angle/360= arc length/2* pie* R
150/360=x/2*3.14*7.5
150/360=x/47.1
360x=7065
x=7065/360
x=19.625 in
8 0
3 years ago
In Richmond, Chloe ordered $40 worth of sushi. She knew that when the bill came, she would need to pay Richmond sales tax for 5%
maks197457 [2]

Answer:

$50

Step-by-step explanation:

Given data

Cost of sushi= $40

Tax= 5%

Tip= 20%

Let us find the amount of the tax and the tip

Tax

=5/100*40

=0.05*40

=$2

Tip

=20/100*40

=0.2*40

=$8

Hence the total amount paid is

=40+2+8

=$50

6 0
3 years ago
Other questions:
  • How do I make 105 over 8 a mixed number
    9·1 answer
  • It cost Tristan $5.60 to send 112 text messages. How much would it cost to send 87
    14·2 answers
  • Explain how to use a model to show 2/6 ÷ 1/12 and 2/6 ÷ 4
    12·1 answer
  • The sum of the angles of a triangle is 180 degrees. Angle Bis 10 degrees more than twice the size of angle A. Angle C is 30 degr
    14·1 answer
  • A car is driving at 70 kilometers per hour. How far, in meters, does it travel in 5 seconds?
    15·1 answer
  • 27+6+23+45+7^3+4+20^6
    14·1 answer
  • I need help please I forgot how to do this
    5·2 answers
  • I WILL GIVE BRAINLY
    9·1 answer
  • A truck that has a mass of 2900kg and is moving down a hill that is 5 m high. What is the potential energy?
    6·1 answer
  • ammy the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the o
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!