Anyone happen to know this answer ?

Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric

mariarad [96]

Answer:

$\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}$

Step-by-step explanation:

Given: (8,-15) is on the terminal ray of angle

To find: All the trigonometric ratios

Solution:

Trigonometry is a branch of mathematics that explain relationship between the sides and angles of triangles.

If (x, y) lies on the terminal side of θ then $r=\sqrt{x^2+y^2}$

$r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17$ units

$\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan \theta}=\frac{-8}{15}$

6 0

3 years ago

The area of a square garden is 25 m2 how long is each side of the garden

Arisa [49]

Answer:

5 meters

Step-by-step explanation:

The area of a square is found by multiplying 2 sides.

If we already have the area, we can take the square root of it to find a side.

√25= 5

All of the sides of a square are the same, therefore each side of the garden is 5 meters long!

7 0

3 years ago

There were m visitors in an exhibition on the first day and 1,200 fewer vistors on the second day. On the third day, the number

STALIN [3.7K]

Answer:

Step-by-step explanation:

The average number is given by :

[m + (m - 1200) + (m - 1200)(1.30 ] / 3 =

[ 2m + 1.30m - 1200 - 1560] / 3 =

[3.3m - 2760] / 3 =

[1.1 m - 920 ]

6 0

3 years ago

Two numbers are in the ratio 5: 6. If the sum of the numbers is 77, find the value of the larger number.

Lynna [10]

Answer:

42

Step-by-step explanation:

sum the parts of the ratio, 5 + 6 = 11 parts

Divide the sum by 11 to find the value of one part of the ratio.

77 ÷ 11 = 7 ← value of 1 part of the ratio , thus

6 parts = 6 × 7 = 42 ← larger number

3 0

3 years ago

What is the prime factorization of 440?

lawyer [7]

Answer:

I would say the correct answer is 2^3 • 5 • 11

Step-by-step explanation:

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

<u>Let's start by dividing 440 by 2 </u>

440 ÷ 2 = 220 - No remainder! 2 is one of the factors!

220 ÷ 2 = 110 - No remainder! 2 is one of the factors!

110 ÷ 2 = 55 - No remainder! 2 is one of the factors!

55 ÷ 2 = 27.5 - There is a remainder. We can't divide by 2 even anymore. Let's try the next prime number

55 ÷ 3 = 18.3333 - This has a remainder. 3 is not a factor.

55 ÷ 5 = 11 - No remainder! 5 is one of the factors!

11 ÷ 5 = 2.2 -There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number

11 ÷ 7 = 1.5714 - This has a remainder. 7 is not a factor.

11 ÷ 11 = 1 - No remainder! 11 is one of the factors!

If we put all of it together we have the factors 2 x 2 x 2 x 5 x 11 = 440. It can also be written in exponential form as 2^3 x 5^1 x 11^1.

here is also the factor tree method : -

7 0

3 years ago