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sesenic [268]
2 years ago
14

The graph of a function is shown:

Mathematics
1 answer:
Sphinxa [80]2 years ago
6 0

Answer:

B.

Step-by-step explanation:

Use (X, Y)

X being the horizontal line

Y being the vertical line

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A. In two or more complete sentences, explain how to find the exact value of sec 13pi/6 including quadrant location
Sergio039 [100]

Answer:

A. The exact value of sec(13π/6) = 2√3/3

B. The exact value of cot(7π/4) = -1

Step-by-step explanation:

* Lets study the four quadrants

# First quadrant the measure of all angles is between 0 and π/2

  the measure of any angle is α  

∴ All the angles are acute  

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between π/2 and π

  the measure of any angle is π - α

∴ All the angles are obtuse

∴ The value of sin(π - α) only is positive

  sin(π - α) = sin(α)  ⇒ csc(π - α) = cscα

  cos(π - α) = -cos(α)   ⇒ sec(π - α) = -sec(α)

  tan(π - α) = -tan(α)   ⇒ cot(π - α) = -cot(α)

# Third quadrant the measure of all angles is between π and 3π/2

  the measure of any angle is π + α  

∴ All the angles are reflex  

∴ The value of tan(π + α) only is positive

  sin(π + α) = -sin(α)  ⇒ csc(π + α) = -cscα

  cos(π + α) = -cos(α)   ⇒ sec(π + α) = -sec(α)

  tan(π + α) = tan(α)   ⇒ cot(π + α) = cot(α)

# Fourth quadrant the measure of all angles is between 3π/2 and 2π  

  the measure of any angle is 2π - α  

∴ All the angles are reflex

∴ The value of cos(2π - α) only is positive

  sin(2π - α) = -sin(α)  ⇒ csc(2π - α) = -cscα

  cos(2π - α) = cos(α)   ⇒ sec(2π - α) = sec(α)

  tan(2π - α) = -tan(α)   ⇒ cot(2π - α) = -cot(α)

* Now lets solve the problem

A. The measure of the angle 13π/6 = π/6 + 2π

- The means the terminal of the angle made a complete turn (2π) + π/6

∴ The angle of measure 13π/6 lies in the first quadrant

∴ sec(13π/6) = sec(π/6)

∵ sec(x) = 1/cos(x)

∵ cos(π/6) = √3/2

∴ sec(π/6) = 2/√3 ⇒ multiply up and down by √3

∴ sec(π/6) = 2/√3 × √3/√3 = 2√3/3

* The exact value of sec(13π/6) = 2√3/3

B. The measure of the angle 7π/4 = 2π - π/4

- The means the terminal of the angle lies in the fourth quadrant

∴ The angle of measure 7π/4 lies in the fourth quadrant

- In the fourth quadrant cos only is positive

∴ cot(2π - α) = -cot(α)

∴ cot(7π/4) = -cot(π/4)

∵ cot(x) = 1/tan(x)

∵ tan(π/4) = 1

∴ cot(π/4) = 1

∴ cot(7π/4) = -1

* The exact value of cot(7π/4) = -1

5 0
3 years ago
1. 248 + 56 base 8 2. 751 +24 base 4 3. 1001 _ 111 base 3 4.3121 _1334 base 5 5. 321 ×21 base 5 6. 205+ 51 base 6​
liraira [26]

Answer:

If we are converting between two bases other than decimal, we typically have to convert ... For two digits in base 8, we need 4, 5, or 6 digits in base 2.

5 0
3 years ago
Select five numbers that have 7, 13, and 3 as prime factors.
MaRussiya [10]

Answer:

ADFGH

Step-by-step explanation:

Good luck on your test!

5 0
2 years ago
Read 2 more answers
Point B has coordinates (-2,-5). After a translation 4 units down, a reflection across the y-axis, and a
Ratling [72]

Answer:

2, -3

Step-by-step explanation:

4 units down is -9, then a reflection over y axis makes -2 2 6 units up makes -9 -3

5 0
3 years ago
A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An it
Vesna [10]

Divide the restocking fee by the price of the item:


12/200 = 0.06

9/150 = 0.06

Multiply by 100 to get the percent:

0.06 x 100 = 6%

Answer: 6%

3 0
2 years ago
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