Tan (Ф/2)=⁺₋√[(1-cosФ)/(1+cosФ)]
if π<Ф<3π/2;
then, Where is Ф/2??
π/2<Ф/2<3π/4; therefore Ф/2 is in the second quadrant; then tan (Ф/2) will have a negative value.
tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]
Now, we have to find the value of cos Ф.
tan (Ф)=4/3
1+tan²Ф=sec²Ф
1+(4/3)²=sec²Ф
sec²Ф=1+16/9
sec²Ф=(9+16)/9
sec²Ф=25/9
sec Ф=-√(25/9) (sec²Ф will have a negative value, because Ф is in the sec Ф=-5/3 third quadrant).
cos Ф=1/sec Ф
cos Ф=1/(-5/3)
cos Ф=-3/5
Therefore:
tan(Ф/2)=-√[(1-cosФ)/(1+cosФ)]
tan(Ф/2)=-√[(1+3/5)/(1-3/5)]
tan(Ф/2)=-√[(8/5)/(2/5)]
tan(Ф/2)=-√4
tan(Ф/2)=-2
Answer: tan (Ф/2)=-2; when tan (Ф)=4/3
The general formula for the distance between two points is
Anyway, if A and B have the same x or y coordinates, this formula can be simplified. For example, in this case the two points have the same x coordinate of -8, so the following part of the formula simplifies:
So, we're left with
but the square root of a square is the absolute value of the object being squared:
which is this case means 
which is the correct length of the side.
Answer:
y - 13 = (5/2)(x - 4)
Step-by-step explanation:
Here we know the slope and one point on the line. Use the point-slope formula:
y - k = m(x - h).
Substituting 13 for k, 4 for x and 2.5 for m, we get:
y - 13 = (5/2)(x - 4)
In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ; this is not sufficient to prove triangles DEF and OPQ congruent through SAS
<h3>What are
congruent triangles?</h3>
Two triangles are said to be congruent if they have the same shape, all their corresponding angles as well as sides must also be congruent to each other.
Two triangles are congruent using the side - angle - side congruency if two sides and an included angle of one triangle is congruent to that of another triangle.
In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ; this is not sufficient to prove triangles DEF and OPQ congruent through SAS
Find out more on congruent triangle at: brainly.com/question/1675117
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