All categories

3 years ago

Find tan Ø, given that sin Ø = - 4/5 and cos Ø>0.

Mathematics

1 answer:

Contact [7]3 years ago

5 0

Answer:

Option 2). -4/3 is the correct answer

Step-by-step explanation:

It is given that,

sin Ø = - 4/5 and cos Ø>0.

sin Ø = opposite side/hypotenuse = - 4/5

Adjacent side = square root (hypotenuse² - opposite side²)

= square root (5² - 4²) = √9 = +3 or -3

cos Ø =Adjacent side/hypotenuse

It is given that, cos Ø>0

cos Ø = 3/5

Therefore tan Ø = Opposite side/Adjacent side = 4/3 or -4/3

The second option is the correct answer -4/3

You might be interested in

Determine the slope and y-intercept of each graph. Then, write the equation of the graph in slope-intercept form.

Eva8 [605]

Answer:

-3/2=slope

y-int = (0,1)

Equation= Y=-3/2x+1

Step-by-step explanation:

7 0

3 years ago

What is the answer to 9x-7i>3(3x-7u)

Jlenok [28]

Answer:

undefined

Step-by-step explanation:

3 0

3 years ago

He sum of two numbers is 43 and the difference is 5. What are the numbers ?

lord [1]

Answer:

24,19

Step-by-step explanation:

24+19=43

24-19=5

4 0

3 years ago

Find the distance between the two points rounding to the nearest tenth (if necessary). (2,−3) and (0,−8)

saveliy_v [14]

Answer:

square root of 29

Step-by-step explanation:

use the distance formula and then plug the numbers in, i got the sqrt(29) after i did that

6 0

3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago