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Pani-rosa [81]
3 years ago
5

What is sin θ given (–3, 4) is a point on the terminal side of θ?

Mathematics
1 answer:
Ber [7]3 years ago
5 0

Answer:

QUESTION 1-  sin\theta =-\frac{4}{5}

QUESTION 2-  cos\theta =-\frac{5}{\sqrt{14} }

QUESTION3- sinx =-\frac{1}{\sqrt{17} }

Step-by-step explanation:

For Question 1

From the given point(-3,4), we can deduce the following.


The point is in the 2nd quadrant.

The right-angled triangle which is formed has a hypotenuse of length 5 by Pythagoras theorem whrere B=3 and P=4.


The third quadrant are from 90° to 180° in which the angle lie.

so  sin\theta =-\frac{P}{H}=-\frac{4}{5}


For Question 2

From the given point(-4,-5), we can deduce the following.


The point is in the 3rd quadrant.

The right-angled triangle which is formed has a hypotenuse of length  \sqrt{14} by Pythagoras theorem whrere B=-4 and P=-5.

The third quadrant are from 180° to 270° in which the angle lie.

so  cos\theta =-\frac{P}{H} =-\frac{5}{\sqrt{14} }


For Question 3

The line with equation 4b + a = 0 , we can deduce that the value of b=-\frac{a}{4}

slope of line  tan\theta =-\frac{P}{B} =-\frac{1}{4}

Hypotenuse of length \sqrt{17} by Pythagoras theorem whrere B=4and P=1.

so  sinx =-\frac{P}{H} =-\frac{1}{\sqrt{17} }.


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1 1/2 is the correct answer
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3 years ago
Write the equation of a line in point slope form that is PARALLEL 5x + 2y = 1 that passes through the point (- 2, - 3) .
aliya0001 [1]

Answer:

y = -5/2x - 13

Step-by-step explanation:

First, we have to find the slope of the original equation

Subtract 5x from both sides

5x + 2y = 1

- 5x         - 5x

2y = -5x + 1

Divide both sides by 2

2y/2 = (-5x + 1)/2

y = -5/2x + 1/2

The slope of this equation is -5/2, so -5/2 has to be in our new parallel equation

y = -5/2x + b

Plug in the given x and y

-3 = -5/2(-2) + b

-3 = 10 + b

Subtract 10 from both sides

-3 = 10 + b

- 10  - 10

b = -13

This makes our equation: y = -5/2x - 13

7 0
3 years ago
Mark read 2 1/2 books last week. This week he read 3 1/3 books. How many more books did Mark read this week and last week?
nikklg [1K]

Answer:

5/6 books

Step-by-step explanation:

We know that Mark read 2 1/2 books last week. This week, he read a bit more with 3 1/3 books.

To find how many more books he read, we must subtract 2 1/2 from 3 1/3:

3 1/3 - 2 1/2

Let's convert these into improper fractions first:

3 1/3 = (3 * 3 + 1) / 3 = 10/3

2 1/2 = (2 * 2 + 1) / 2 = 5/2

Now, we have:

10/3 - 5/2

In order to subtract these, we must find a common denominator. For 2 and 3, the LCM is 6, so we can use that as our common denominator:

10/3 * 2/2 = 20/6

5/2 * 3/3 = 15/6

Finally, we have:

20/6 - 15/6 = (20 - 15) / 6 = 5/6 books

5 0
3 years ago
Find the following measure for this figure.<br> Volume =
Rudiy27

Answer:

400 cubic units

Step-by-step explanation:

The volume of a square prism is \dfrac{1}{3} s^2 h. Plugging in the given values, you get:

\dfrac{1}{3}\cdot 10^2 \cdot 12= 400

Hope this helps!

5 0
3 years ago
Can you tell me a quick way to solve this problem 2/7m-1/7=3/14
skad [1K]
<span>2/7m-1/7=3/14
make the denominators equal and to this just multiply the denominators of the first two equations by 2 but you have to multiply the numerators too and by the same value
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with the denominators equal, you can delete them

4m-2=3
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4m=5
m=5/4</span>
3 0
3 years ago
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