All categories

3 years ago

Use the given information to determine the exact trigonometric value.

Mathematics

1 answer:

hoa [83]3 years ago

6 0

Answer:

Step-by-step explanation:

Use the main trigonometric equality:

$\cos ^2\theta+\sin^2\theta=1.$

Since $\sin\theta=-\dfrac{1}{5},$ you have that

$\cos^2\theta=1-\left(-\dfrac{1}{5}\right)^2=1-\dfrac{1}{25}=\dfrac{24}{25}.$

You know that $\pi$ thus $\cos \theta$

and

$\cos\theta=-\sqrt{\dfrac{24}{25}}=-\dfrac{2\sqrt{6}}{5}.$

You might be interested in

Given right triangle A w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle B, w/ a hypotense length of y+5 and

SpyIntel [72]

Triangle A

hypotenuse: 3y + x
leg: y - x

Triangle B

hypotenuse: y + 5
leg: x + 5

Congruency => 3y + x = y + 5 and y - x = x + 5

Solve the system

3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5

2y + x = 5
-2y + 4x = -10

5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3

Verify:

hypotenuses
3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8

Legs:

y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.

Then both hypotenuses and both legs are congruent.

Answer: x = -1 and y = 3

4 0

3 years ago

Given: 4x=12x+32 prove: =-4

myrzilka [38]

Answer:

See explanation

Step-by-step explanation:

4x = 12x + 32

Subtract 12x from both sides

-8x = 32

Divide each side by -8.

x = -4

6 0

2 years ago

Read 2 more answers

The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units

ad-work [718]

Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&C&(~ 6 &,& 2~)
\end{array}~~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}
\\\\\\
AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}
\\\\\\
AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&B&(~ 16 &,& 2~)
\end{array}\\\\\\
AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}
\\\\\\
AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}
\\\\\\
AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}$

so, add AC + AB + CB, and that's the perimeter of the triangle.

8 0

3 years ago

If a aquadrilateral is equiangular, then it coul be a .....

kupik [55]

Answer:

Square

Answer A is correct

8 0

3 years ago

Read 2 more answers

Pls only answer if yk it ill give correct one BRAINLIEST!!

Dmitry [639]

Answer:

X=10, x=4

Step-by-step explanation:

first, divide 14 by 2, and square it; giving you

x^2-14x+(7)^2=-40

Because 7^2 is 49, you have to add 49 to the other side; giving you

x^2-14x+(7)^2=9

Then factor the left side; giving you (x-7)^2=9

Take the square root of both sides, giving you

(x-7)^2= plus or minus 3

Then solve to get two solutions, 10 and 4

8 0

3 years ago