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
Mariana [72]
3 years ago
15

Find the remaining trigonometric ratios. tan(α) = 2, 0<α<π/2the responses they want are:1. sine(α)=_2. cos(α)=_3. cot(α)=_

4. sec(α)=_5. csc(α)=_
Mathematics
1 answer:
Andreas93 [3]3 years ago
7 0

Answer:

1. sinα = +2√5/5 2.  cosα = +√5/5 3. cotα = +1/2 4. secα = +√5 5. cosecα = +√5/2.

Step-by-step explanation:

1. Since tan(α) = 2 and 1 + cot²α = cosec²α

1 + 1/tan²α = 1/sin²α

1 + 1/2² = 1/sin²α

1 + 1/4 = 1/sin²α

5/4 = 1/sin²α

sinα = ±√(4/5)

sinα = ±2/√5

sinα = ±2√5/5

Since 0<α<π/2, sinα = +2√5/5

2. sin²α + cos²α = 1

(2/√5)² + cos²α = 1

4/5 + cos²α = 1

cos²α = 1 - 4/5

cos²α = 1/5

cosα = ±1/√5

cosα = ±√5/5

Since 0<α<π/2, cosα = +√5/5

3. cotα = 1/tanα = 1/2

Since 0<α<π/2, cotα = +1/2

4. secα = 1/cosα = 1/±1/√5 = ±√5

Since 0<α<π/2, secα = +√5

5. cosecα = 1/sinα = 1/±2/√5 = ±√5/2

Since 0<α<π/2, cosecα = +√5/2

You might be interested in
10) A rhombus has a<br> diagonal 8.6 mm long<br> and an area of 81.7 mm. what is the<br> perimeter?
BaLLatris [955]

Answer:

P=41.72

Step-by-step explanation:

S=ACxDB/2

81.7=8.6xDB/2

81.7=4.3xDB|:4.3

19(mm)=DB

DO=19/2=9.5

OC=8.6/2=4.3

(O is the center of the rhombus, where two diagonals meet)

a²+b²=c² (DO²+OC²=DC²)

9.5²+4.3²=c²

90.25+18,49=c²

√108,74=√c²

c≈10.43

P=4c

P=4x10.43

P=41.72

Hope it helps:)

6 0
2 years ago
A car advertisement states that a certain car can accelerate from rest to 70 m/s in 7 seconds. Find the car's average accelerati
Contact [7]

Answer:

The average acceleration of the car will be 10 m/s.

Step-by-step explanation:

70 / 7 = 10 m/s.

5 0
3 years ago
Last year there were 1,435 8th grade students enrolled at your sc hool. This year there are 1,220. What is the percent change in
Elanso [62]

1.2% of 8th grade students is the percentage change.

3 0
3 years ago
if the first two statements are true, is the third statement true? 1. all dogs like walks. 2. bandit doesn't like walks. 3. band
Strike441 [17]

If the first two statements are true, then the third statement:

"Bandit is not a dog"

Is true.

<h3>if the first two statements are true, is the third statement true?</h3>

The first statement is:

P = "All dogs like walks"

We assume that this is true, so, if X is a dog, X likes walks.

The second statement is:

Q = "Bandit doesn't like walks"

From this, we only can conclude that Bandit doesn't like walks.

And all dogs like walks, so if Bandit were a dog, he would like walks, but because he does not like walks, we can conclude that Bandit is not a dog.

From that, the third statement:

K = "Bandit is not a dog"

Is true.

So we write that as a conditional statement:

If P and Q ⇒ K

<em>"if all dogs like walks, and Bandit doesn't like walks, then bandit is not a dog".</em>

If you want to learn more about conditional statements:

brainly.com/question/11073037

#SPJ1

3 0
1 year ago
What is the sum of the interior angles of a nonagon?
SSSSS [86.1K]
To find the sum of the interior angles of a nonagon, divide it up into triangles... There are seven triangles... Because the sum of the angles of each triangle is 180 degrees... We get

7 * 180 = 1260°

So, the sum of the interior angles of a nonagon is 1260 degrees.

3 0
3 years ago
Read 2 more answers
Other questions:
  • an investment of $5000 earned $1050 for 1 year. How much will an investment of $9000 earn at the same rate for 1 year?​
    5·1 answer
  • Please help meeeeee cuz i don’t know itttt and it’s due soon
    9·1 answer
  • How can I use models to add fractions?
    12·1 answer
  • Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2)
    7·1 answer
  • a local theater sells admission tickets for $9.00 on Thursday nights. at capacity , the theater holds 100 customers. the functio
    5·2 answers
  • W - 4 &gt; 9 on a coordinate plane
    10·1 answer
  • How do you solve this problem?
    10·1 answer
  • Find the value of x (please help)
    13·1 answer
  • A chorus has 5 girls and 15 boys. If two are chosen at random to sing a duet, what is the probability that both will be boys?
    12·2 answers
  • Eddie is paid $17.25 per hour for a regular 37-hour week. His overtime rate is 1 1/2 times his regular hourly rate. Use his time
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!