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
emmasim [6.3K]
3 years ago
12

What are the exact values of the six trigonometric functions for -7pi/6 radians?

Mathematics
2 answers:
laiz [17]3 years ago
7 0
Sin -7π/6 = 0.5
cos -7π/6 = -√3/2
tan -7π/6 = -1/√3
sec -7π/6 = -2/√3
csc -7π/6 =2
cot -7π/6 = -√3

note: -7π/6 radians = -210° degree = -210 +360 = 150° = 5π/6

I have attached the unit circle for the given angle

prohojiy [21]3 years ago
4 0
For -7pi/6 is an angle in second quadrant, then sine and cosecant must be positive; and cosine, secant, tangent and cotangent must me negative.
The reference angle is:
7pi/6-pi=7pi/6-6pi/6=(7pi-6pi)/6=pi/6
Then
sin(-7pi/6)=sin(pi/6)→sin(-7pi/6)=1/2

cos(-7pi/6)=-cos(pi/6)→cos(-7pi/6)=-sqrt(3)/2

csc(-7pi/6)=1/sin(-7pi/6)=1/(1/2)=1(2/1)=2/1→csc(-7pi/6)=2

sec(-7pi/6)=1/cos(-7pi/6)=1/(-sqrt(3)/2)=-1(2/sqrt(3))=-2/sqrt(3)→
sec(-7pi/6)=-[2/sqrt(3)]*sqrt(3)/sqrt(3)=-2sqrt(3)/[sqrt(3)]^2→
sec(-7pi/6)=-2sqrt(3)/3

tan(-7pi/6)=sin(-7pi/6)/cos(-7pi/6)=(1/2)/(-sqrt(3)/2)=-(1/2)*(2/sqrt(3))→
tan(-7pi/6)=-2/[2sqrt(3)]=-1/sqrt(3)=-[1/sqrt(3)]*[sqrt(3)/sqrt(3)]→
tan(-7pi/6)=-sqrt(3)/[sqrt(3)]^2→tan(-7pi/6)=-sqrt(3)/3

cot(-7pi/6)=cos(-7pi/6)/sin(-7pi/6)=[-sqrt(3)/2]/(1/2)=-sqrt(3)/2*(2/1)→
cot(-7pi/6)=-2sqrt(3)/2→cot(-7pi/6)=-sqrt(3)

Answers:
sin(-7pi/6) = 1/2
cos(-7pi/6) = - sqrt(3)/2
tan(-7pi/6) = - sqrt(3)/3
csc(-7pi/6) = 2
sec(-7pi/6) = - 2*sqrt(3)/2
cot(-7pi/6) = - sqrt(3)

You might be interested in
Find the unknown. = (65 × 3) + 9
alekssr [168]

Answer:

204

Step-by-step explanation:

Following the order of operations, what is within the parenthesis is solved first.

<em>65 x 3 = 195</em>

Then, you add 9 to 195.

<em>195 + 9 = 204</em>

<em>204</em> is the final answer.

Have a nice day! ^-^

5 0
3 years ago
PLEASE HELP ILL GIVE BRAINLIEST
dusya [7]

1)

(-2+\sqrt{-5})^2\implies (-2+\sqrt{-1\cdot 5})^2\implies (-2+\sqrt{-1}\sqrt{5})^2\implies (-2+i\sqrt{5})^2 \\\\\\ (-2+i\sqrt{5})(-2+i\sqrt{5})\implies +4-2i\sqrt{5}-2i\sqrt{5}+(i\sqrt{5})^2 \\\\\\ 4-4i\sqrt{5}+[i^2(\sqrt{5})^2]\implies 4-4i\sqrt{5}+[-1\cdot 5] \\\\\\ 4-4i\sqrt{5}-5\implies -1-4i\sqrt{5}

3)

let's recall that the conjugate of any pair a + b is simply the same pair with a different sign, namely a - b and the reverse is also true, let's also recall that i² = -1.

\cfrac{6-7i}{1-2i}\implies \stackrel{\textit{multiplying both sides by the denominator's conjugate}}{\cfrac{6-7i}{1-2i}\cdot \cfrac{1+2i}{1+2i}\implies \cfrac{(6-7i)(1+2i)}{\underset{\textit{difference of squares}}{(1-2i)(1+2i)}}} \\\\\\ \cfrac{(6-7i)(1+2i)}{1^2-(2i)^2}\implies \cfrac{6-12i-7i-14i^2}{1-(2^2i^2)}\implies \cfrac{6-19i-14(-1)}{1-[4(-1)]} \\\\\\ \cfrac{6-19i+14}{1-(-4)}\implies \cfrac{20-19i}{1+4}\implies \cfrac{20-19i}{5}\implies \cfrac{20}{5}-\cfrac{19i}{5}\implies 4-\cfrac{19i}{5}

7 0
3 years ago
Read 2 more answers
Help Please, im stuck on this question.
lions [1.4K]

Answer:

irrational

Step-by-step explanation:

3/4 + sqrt(2)

3/4 is rational

sqrt(2) is irrational

The sum of a rational and an irrational number is irrational

8 0
3 years ago
What single transformation was applied to triangle A to get triangle B? *
irakobra [83]

Answer: dilation

Step-by-step explanation:

the others are rigid transformations, the can’t change the size of the triangle.

6 0
3 years ago
3a + 2b, when a = 10 and b= 5
tia_tia [17]

Answer:

40

Step-by-step explanation:

3a + 2b =

3(10) + 2(5)

30 + 10 = 40

I hope this helps!

Have a great day!

8 0
2 years ago
Read 2 more answers
Other questions:
  • Find the product <br> -12 • (-2) <br><br> A. 10<br><br> B. 24 <br><br> C. -24<br><br> D. -14
    11·1 answer
  • PLEASE ASSIST ME WITH THIS
    9·2 answers
  • A cube has a volume of 7 to the 3rd power cubic centimeters . what is its surface area?
    15·1 answer
  • Xiaoming is making cookies. Each batch of cookies uses3 eggs. If Xiaoming has 20 eggs, and assuming he has enough of the other i
    14·1 answer
  • Elizabeth has 1.32 pounds of candy. She wants to share it equally with herself and 3 friends. How much candy will each person re
    7·1 answer
  • A lottery has 53 numbers from which seven are selected. What is the probability of picking all seven numbers?
    14·2 answers
  • How to Write twenty-four hundredths as a simplified fraction.
    11·1 answer
  • A plumber and his assistant work together to replace the pipes in an old house. The plumber charges $30 an hour for his own labo
    15·1 answer
  • PLEASEEEE HELP ME
    9·1 answer
  • Estimate the value 98.5times 13
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!