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
jasenka [17]
3 years ago
7

The point (1/3,1/4) lies on the terminal said of an angle. Find the exact value of the six trig functions and explain which func

tions are reciprocal functions to each other

Mathematics
1 answer:
katrin2010 [14]3 years ago
3 0

Answer:

sine and cosec are inverse of each other.

cosine and sec are inverse of each other.

tan and cot are inverse of each other.

Step-by-step explanation:

Given point on terminal side of an angle (\frac{1}{3},\frac{1}4).

Kindly refer to the attached image for the diagram of the given point.

Let it be point A(\frac{1}{3},\frac{1}4)

Let O be the origin i.e. (0,0)

Point B will be (\frac{1}{3},0)

Now, let us consider the right angled triangle \triangle OBA:

Sides:

Base, OB = \frac{1}{3}\\Perpendicular, AB = \frac{1}{4}

Using Pythagorean theorem:

\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OA^{2} = OB^{2} + AB^{2}\\\Rightarrow OA^{2} = \frac{1}{3}^{2} + \frac{1}{4}^{2}\\\Rightarrow OA = \sqrt{\frac{1}{3}^{2} + \frac{1}{4}^{2}}\\\Rightarrow OA = \sqrt{\frac{4^2+3^2}{3^{2}.4^2 }}\\\Rightarrow OA = \frac{5}{12}

sin \angle AOB = \dfrac{Perpendicular}{Hypotenuse}

\Rightarrow sin \angle AOB = \dfrac{\frac{1}{4}}{\frac{5}{12}}\\\Rightarrow sin \angle AOB = \dfrac{3}{5}

cos\angle AOB = \dfrac{Base}{Hypotenuse}

\Rightarrow cos \angle AOB = \dfrac{\frac{1}{3}}{\frac{5}{12}}\\\Rightarrow cos\angle AOB = \dfrac{4}{5}

tan\angle AOB = \dfrac{Perpendicular}{Base}

\Rightarrow tan\angle AOB = \dfrac{3}{4}

cosec \angle AOB = \dfrac{Hypotenuse}{Perpendicular}

\Rightarrow cosec\angle AOB = \dfrac{5}{3}

sec\angle AOB = \dfrac{Hypotenuse}{Base}

\Rightarrow sec\angle AOB = \dfrac{5}{4}

cot\angle AOB = \dfrac{Base}{Perpendicular}

\Rightarrow cot\angle AOB = \dfrac{4}{3}

You might be interested in
PLEASEEEEE help I me I will give you BRAINLEST!!!
Tasya [4]

Answer:

(-2,-2)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Ajay is on the swim team. He improved his time on
ozzi

Answer:

<u>5%</u>

Step-by-step explanation

50/32= 1.56yard per second        ; 50/31= 1.61 yard per second

1.61-1.56= 0.05* 100= 5%

5 0
3 years ago
Help please no bias answers
notka56 [123]

Answer:

882 square inches

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
In the monthly payment formula , what value would you put for r if the interest rate is 5.7%?
natulia [17]
In the monthly payment formula r is the percentage rate as a decimal.

To turn a percentage into a decimal, move the decimal point 2 places to the left.
 5.7% becomes 0.057

3 0
3 years ago
Read 2 more answers
Which structures secrete chemicals utilized for the completion of digestion within the small intestine?
Sever21 [200]

Answer:

In the small intestine more digestive enzymes act on the food. Pancreatic juice, from the pancreas, and bile, produced in the liver and stored in the gall bladder, continue to break down various parts of the food. They complete the digestion of starches, sugars, and fats. I hope tis helps

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Distance between Train 1 and Train 2 = 95 miles. Average speed of Train 1 = 45 mph. Average speed of Train 2 = 60 mph. Train 1 i
    7·2 answers
  • a plumber worked at a house on two diffrent days. on the first day, the plumber worked for 5/8 of an hour, on the second day the
    8·1 answer
  • a quilt has 18 squares. 1/3 of the squares are blue. what other fractions represent the blue squares?
    11·2 answers
  • How can you write the equation for a linear function if you
    7·1 answer
  • You read online that a 15 ft by 20 ft would cost about $2,275 to have professionally installed. Estimate the cost of having a 13
    12·1 answer
  • I need help with these 6 problames
    10·1 answer
  • Brainiest to correct answer<br><br> 7 (3x - 2)
    12·2 answers
  • A puppy's weight is 5 pounds at 25% of its full weight. How much does the puppy weigh when fully grown?
    10·2 answers
  • What is the value of 3^ -2 as a fraction
    10·1 answer
  • Graph y=|3x| using as many points as needed
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!