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
Scorpion4ik [409]
11 months ago
14

Find the six trig function values of the angle 240*Show all work, do not use calculator

Mathematics
1 answer:
-BARSIC- [3]11 months ago
5 0

Solution:

Given:

240^0

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

sin240^0=sin(180+60)

Using the trigonometric identity;

sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny

Hence,

\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

cos240^0=cos(180+60)

Using the trigonometric identity;

cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny

Hence,

\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

tan240^0=tan(180+60)

Using the trigonometric identity;

tan(180+x)=tan\text{ }x

Hence,

\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\  \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}

To get cosec 240 degrees:

\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}

To get sec 240 degrees:

\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

To get cot 240 degrees:

\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\  \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}

You might be interested in
What does (2 + 3) + 42 x (5 − 3) =
stellarik [79]

Answer:

5b-2=18

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
At the end of 10 basketball games, a teams mean score is 35 points per game. At the end of 11 games, their mean score has gone d
morpeh [17]

Their total points for the first 10 games were

(10) x (35) = 350 total .

Their total points after 11 games were

(11) x (33) = 363 total .

They must have scored (363 - 350) = 13 points in that 11th game.

I hate to say it, but these kids and their coach are in the wrong game.

4 0
2 years ago
What is the name of the relationship between ∠1 and ∠4 ? corresponding angles alternate exterior angles alternate interior angle
Maslowich
< 1 and < 4 are alternate interior angles
4 0
3 years ago
Read 2 more answers
Jo is thinking of a number. Four less than 9 times the number is 176. Find Jo’s number
kondaur [170]

Answer:

Jo's Number is 20.

Step-by-step explanation:

4 - ( 9 x ? ) = 176.

9 x 20 = 180.

9 x 20 = 180, then subtract 180 by 4.

180 - 4 = 176.

Therefore, Jo's number is 20.

5 0
2 years ago
What transformations can be used to show two figures are congruent?
Zinaida [17]
Translation rotation reflection
7 0
3 years ago
Other questions:
  • What is the prime factorization of 102
    7·1 answer
  • Jared earned $55 from cleaning pools. He deposits the $55 into his checking account.
    13·1 answer
  • How to solve number 13
    11·1 answer
  • You are a telemarketer. You can expect that 2% of your calls will result in a sale. You make 50 calls before lunch.
    6·2 answers
  • According to a 2013 study by the Pew Research Center, 15% of adults in the United States do not use the Internet (Pew Research C
    5·1 answer
  • Which comparisons are true? Select all that apply.
    7·1 answer
  • What is the answer for 12=-4b
    15·2 answers
  • The base of a cylinder has an area of 12 cm2. This cylinder has a height of 5 cm. What is the volume of this cylinder? ​
    9·1 answer
  • Someone please help me with this question​
    10·1 answer
  • What is the volume of a triangular prisim if the length is 4cm heigght is 3cm and width is 11cm
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!