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
lions [1.4K]
2 years ago
8

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta​

Mathematics
1 answer:
aleksley [76]2 years ago
6 0

Answer:

sec Θ = \frac{\sqrt{65} }{7}

Step-by-step explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

Since 270° < Θ < 360° ← that is fourth quadrant, then

sec Θ > 0, thus

sec²Θ = (- \frac{4}{7})² + 1 = \frac{16}{49} + 1 = \frac{65}{49}, then

sec Θ = \sqrt{\frac{65}{49} } = \frac{\sqrt{65} }{7}

You might be interested in
A recipe used 2/3 cup of sugar for every 2 teaspoons of butter. How much sugar was used per teaspoon of butter
myrzilka [38]

Answer:

2/3cups 2 teaspoons

(2/3 )cups/2teaspoons =1/3 cups per teaspoon

Answer= 1/3 cups per teaspoon

8 0
3 years ago
Read 2 more answers
The radius of a circle is 18 in what is the area and circumference ​
Inessa05 [86]

Answer:

324 pi .  and 36 pi

Step-by-step explanation:

Area is pi r squared, so 18x18 is 324, times pi which is 324 pi

Circumference is 2 pi r, which is 2 times 18 which is 36, times pi which is 36 pi

:D

7 0
3 years ago
P and Q are two points on the line x - y + 1 = 0 and are at distance 5 from the origin. Find the area of the triangle OPQ. ​
Alecsey [184]

Answer:

P and Q are two points on the line x-y+1=0 and are at a distant of 5 units from the origin. Find the area of triangle POQ.

Step-by-step explanation:

P and Q are the intersection points of

x-y+1 = 0 and the circle x^2 + y^2 = 25

sub y = x+1 into the circle

x^2 + (x+1)^2 = 25

x^2 + x^2 + 2x + 1 - 25 = 0

x^2 + x - 12 = 0

(x+4)(x-3) = 0

x = 3 or x = -4

y = 4 or y = -3

so P(3,4) and Q(-4,3) are our two points

Height of triangle.

h = |0 - 0 + 1|/√2 = 1/√2

PQ = √( (-7)^2 + 1^2) = √50 = 5√2

area POQ = (1/2)(1/√2)(5√2) = 5/2 square units

hope this helped

7 0
2 years ago
Solve (x +1 &lt; 4) n ( x - 8 &gt; -7)?​
Anna007 [38]

X<3 or X>1

move constant to the right side and change the sign

8 0
3 years ago
What information is missing
I am Lyosha [343]

rainfall in mm

Step-by-step explanation:

we cant count water in inches

6 0
2 years ago
Other questions:
  • a wooden box has external dimensions 40 cm by 34 cm by 30 cm. if the wood is 1 cm thick how many cm3 of wood is used in it ?​
    6·2 answers
  • What is the square root of 139
    12·1 answer
  • Jameson is seeking a loan with a simple interest rate of 3% per year. If he wants to borrow $8000, then how much will he be char
    9·1 answer
  • An investor buys 400 shares of stock in a fund when the net asset value is $19.62 and the offer price is $19.84. The investor se
    11·2 answers
  • Which expressions are equivalent to -3 -(7.5+4)
    6·1 answer
  • In the cafeteria 100 milk cartons put out for breakfast. At the end of breakfast 27 remained
    12·2 answers
  • A sector of a circle has an arc length of 8 pi inches and a central angle of 20 degrees, as shown. What is the circumference of
    7·1 answer
  • Anyone down to play nitro type with me?
    8·2 answers
  • Plssssss help number 18 and 20​
    5·2 answers
  • What is what is what is what is 2+2​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!