Answer:
sin
(
x/
2
) = -
√
3
/2
Take the inverse sine of both sides of the equation to extract x
from inside the sine.
x/
2
=
arcsin
(
−
√
3/
2
)
The exact value of arcsin
(
−
√
3
/2
) is −
π
/3
.
/x
2
=
−
π
/3
Multiply both sides of the equation by 2
.
2
⋅
x
/2
=
2
⋅
(
−
π
/3
)
Simplify both sides of the equation.
x
=
−
2
π
/3
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2
π
, to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.
x
/2
=
2
π
+
π/
3
+
π
Simplify the expression to find the second solution.
x
=
2
π
/3
4
π
Add 4
π to every negative angle to get positive angles.
x
=
10
π
/3
The period of the sin
(
x
/2
) function is 4
π so values will repeat every 4
π radians in both directions.
x
=2
π
/3
+
4
π
n
,
10
π/
3
+
4
π
n
, for any integer n
Exclude the solutions that do not make sin
(
x
/2
)
=
−
√
3/
2 true.
x
=
10
π
/3
+
4
π
n
, for any integer n
Answer:
B . Yes
Step-by-step explanation:
Recall: a tangent of a circle is perpendicular to the radius of a circle, forming a right angle at the point of tangency.
Therefore, if segment ST is tangent to circle P, it means that m<T = 90°, and ∆PST is a right triangle.
To know if ∆PST is a right triangle, the side lengths should satisfy the Pythagorean triple rule, which is:
c² = a² + b², where,
c = longest side (hypotenuse) = 37
a = 12
b = 35
Plug in the value
37² = 12² + 35²
1,369 = 1,369 (true)
Therefore we can conclude that ∆PST is a right triangle, this implies that m<T = 90°.
Thus, segment ST is a tangent to circle P.
Hello!
<h3><em><u>Answer</u></em></h3>
The area of the right triangle is 30 
. The perimeter is 40 in.
<h3><em><u>Explanation</u></em></h3>
First, we must find the measure of the hypotenuse of the triangle by using the Pythagorean Theorem.
+ 
64 + 225 = 
√289 =
17 = 
Now that we have all the side lengths, we can use the formulas to find the area and perimeter.
<h3>AREA:</h3>
A = 
A = (15 × 8) ÷ 2
A = 30
<h3>PERIMETER:</h3>
P = a + b + c
P = 8 + 15 + 17
P = 40
Estimate, ok
area=side^2
if we round
25^2=625
25.3 is slighly bigger so maybe 632 squaer centimters or something
The correct answer is b lave flows from a volcano and piles up
