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]
1 year ago
14

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

Mathematics
1 answer:
-BARSIC- [3]1 year 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
Ying is going out to a pasta dinner. There are 5 types of noodles to choose from and 4 choices of vegetable side. How many diffe
slavikrds [6]

Answer:

20

Step-by-step explanation:

After asking so many questions of this type, I hope you understand the way to answer them.

5 types of noodles

4 choices of vegetable sides

Number of different pasta diners = 4 * 5 = 20

3 0
3 years ago
What is the mechanical advantage of a hockey stick that is gripped at point D and hits the puck at point B?
RideAnS [48]

Answer:

Mechanical advantage = Effort distance/Resistance distance

Effort distance = D - Fulcrum = 0.5 m

Resistance distance = A - Fulcrum = 2.0 m

Then,

Mechanical advantage = 0.5/2 = 0.25 

Hockey stick is an example of third class where mechanical advantage is less than one as the speed of the end of point A is critical.

5 0
2 years ago
Read 2 more answers
14. a? +b = c<br>Pythagorean Theorem​
lions [1.4K]

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

a^2 + b^2 = c^2

5 0
3 years ago
Why might your purpose change while you’re reading a passage?
SashulF [63]

Answer is B- you might begin to visualize the story.

6 0
3 years ago
What is the relationship between the symbol and the word pi?
swat32
The distance around the outside a circle is its circumference. Consider the formula for the circumference of a circle, Circumference = Pi x Diameter. Solving for Pi we get, Pi = Circumference divided by Diameter.
4 0
3 years ago
Other questions:
  • PLEASE HELP WITH MY GEOMETRY HOMEWORK
    8·1 answer
  • Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Ann
    12·2 answers
  • Value of 6n-2 when n=3
    6·2 answers
  • An SUV costs $25,535 and costs an average of $0.18 per mile to maintain. A hybrid model of the SUV costs $32,395 and costs an av
    14·1 answer
  • Answer and get brainliest
    10·1 answer
  • What is the circumference, in centimeters, of the circle? Use 3.14 for Pi, show the equation you use as well.
    9·2 answers
  • if melissa placed an order for garden gloves ($2.99 each), and rakes (for $16.99 each), and she ordered three times as many glov
    7·1 answer
  • What is the product of z and 5
    6·1 answer
  • What ia 4(t-5) FAST !!!!!!
    14·2 answers
  • ]
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!