Step-by-step explanation:
The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
How to determine the value of sin(2x)
The cosine ratio is given as:
\cos(x) = -\frac 14cos(x)=−
4
1
Calculate sine(x) using the following identity equation
\sin^2(x) + \cos^2(x) = 1sin
2
(x)+cos
2
(x)=1
So we have:
\sin^2(x) + (1/4)^2 = 1sin
2
(x)+(1/4)
2
=1
\sin^2(x) + 1/16= 1sin
2
(x)+1/16=1
Subtract 1/16 from both sides
\sin^2(x) = 15/16sin
2
(x)=15/16
Take the square root of both sides
\sin(x) = \pm \sqrt{15/16
Given that
tan(x) < 0
It means that:
sin(x) < 0
So, we have:
\sin(x) = -\sqrt{15/16
Simplify
\sin(x) = \sqrt{15}/4sin(x)=
15
/4
sin(2x) is then calculated as:
\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)
So, we have:
\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗
4
15
∗
4
1
This gives
\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
Answer:
5/4
Step-by-step explanation:
Make a proportion:
16/4 = 5/x
Cross Multiply:
20 = 16x
x = 5/4
From the problem we have
In △ABC, m∠A=52°, c=11, and m∠B=19°.
Draw the diagram with the help of given information, (see the attached image)
Now using Sine Law in the Triangle ABC, we can write
Now from Triangle ABC , we can write
Now simplify , we get
Answer:
10.82
Step-by-step explanation:
Answer:
(0, 7]
Step-by-step explanation:
Let's call the width W and the length L. The length is 18 feet more than the width, so:
L = W + 18
The area can be no more than 175, so:
A ≤ 175
LW ≤ 175
Since L = W + 18:
(W + 18) W ≤ 175
W² + 18W ≤ 175
W² + 18W - 175 ≤ 0
(W - 7) (W + 25) ≤ 0
-25 ≤ W ≤ 7
However, the width of the table can't be nonpositive, so:
0 < W ≤ 7
Or in interval notation, (0, 7].