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Oksi-84 [34.3K]
3 years ago
10

Why does one has a line with arrows and the other doesn’t?

Mathematics
1 answer:
12345 [234]3 years ago
8 0
One is a line segment ( it stops)( a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints) and the other is a line that keeps doing
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If θ is an angle in standard position that terminates in Quadrant III such that tanθ = 5/12, then sinθ/2 = _____
babunello [35]

Answer:

sin θ/2=5√26/26=0.196

Step-by-step explanation:

θ ∈(π,3π/2)

such that

θ/2 ∈(π/2,3π/4)

As a result,

0<sin θ/2<1, and

-1<cos θ/2<0

tan θ/2=sin  θ/2/cos θ/2

such that

tan θ/2<0

Let

t=tan θ/2

t<0

By the double angle identity for tangents

2 tan θ/2/1-(tanθ /2)^2  = tanθ

2t/1-t^2=5/12

24t=5 - 5t^2

Solve this quadratic equation for t :

t1=1/5 and

t2= -5

Discard t1 because t is not smaller than 0

Let s= sin θ/2

0<s<1.

By the definition of tangents.

tan θ/2= sin θ/2/ cos θ/2

Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.

cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2

Solve for s.

s/-√1-s^2 = -5

s^2=25(1-s^2)

s=√25/26 = 5√26/26

Therefore

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State the domain and range of the given relation. {(-1,2),(1,2),(3,2),(6,2)}
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Step-by-step explanation: In this problem, we're asked to state the domain and range for the following relation {(-1,2), (1,2), (3,2), (6,2)}.

Let's go over a few vocabulary words and

these are <em>domain</em>, <em>range</em>, and <em>relation</em>.

So let's start with the word <em>relation</em>.

A <em>relation</em> is simply a set of ordered pairs like you see here.

The <em>domain</em> is the set of all x-coordinates for those ordered pairs.

So in this case, the domain is -1, 1, 3, and 6.

We can write this as {-1, 1, 3, 6}.

The <em>range</em> is the set of all y-coordinates for those ordered pairs.

So in this case our range is 2, 2, 2, and 2.

Notice that the y-coordinate of 2 is

repeated in three of our ordered pairs.

In this situation, we only need to mention it once in our range.

So our range is {2}.

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