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Serga [27]
3 years ago
13

If cosine theta equals negative square root of three over two and pi over two less than theta less than pi, what are the values

of sin Θ and tan Θ?
sine theta equals negative one half, tangent theta equals square root of three over three
sine theta equals negative one half, tangent theta equals negative square root of three over three
sine theta equals one half, tangent theta equals negative square root of three over three
sine theta equals one half, tangent theta equals square root of three over three
Mathematics
2 answers:
Natalka [10]3 years ago
7 0
<h2>Answer:</h2>

The values of sinθ and tanθ are:

\sin \theta=\dfrac{1}{2}

and

\tan \theta=-\dfrac{1}{\sqrt{3}}=-\dfrac{\sqrt{3}}{3}

<h2>Step-by-step explanation:</h2>

It is given that:

\cos \theta=-\dfrac{\sqrt{3}}{2}

where

\dfrac{\pi}{2}

i.e. the angle θ lie in the second quadrant.

Also, we know that in the second quadrant sine and cosecant function is positive.

whereas cosine,secant, tangent and cotangent functions are negative.

Now, we know that:

\cos (\dfrac{5\pi}{6})=-\dfrac{\sqrt{3}}{2}

i.e. here

\theta=\dfrac{5\pi}{6}

Hence, we have:

\sin (\theta)=\sin (\dfrac{5\pi}{6})\\\\i.e.\\\\\sin \theta=\dfrac{1}{2}

Also,

\tan \theta=\dfrac{\sin \theta}{\cos \theta}\\\\i.e.\\\\\tan \theta=\dfrac{\dfrac{1}{2}}{\dfrac{-\sqrt{3}}{2}}\\\\i.e.\\\\\tan \theta=\dfrac{1}{-\sqrt{3}}\\\\i.e.\\\\\tan \theta=-\dfrac{1}{\sqrt{3}}

Now, on rationalizing we have:

\tan \theta=-\dfrac{\sqrt{3}}{3}

rosijanka [135]3 years ago
4 0

Answer:

sin θ = 1/2

tan θ = -√3 / 3

Step-by-step explanation:

cos θ = -√3 / 2, π/2 < θ < π

θ is in the second quadrant, so θ = 5π/6.

sin θ = 1/2

tan θ = sin θ / cos θ = -√3 / 3

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Free_Kalibri [48]

The number of stamps with penny in terms of x is \frac{x}{6}

<em><u>Solution:</u></em>

Given that,

Ryan has x stamps in his collection

Number of stamps of Ryan = x stamps

Let the stamps with penny be "a"

Ryan has 6 times as many stamps as penny

Therefore,

Number of stamps in Ryan = 6 times as many stamps as penny

\text{Number of stamps in Ryan } = 6 \times a\\\\x = 6a\\\\a = \frac{x}{6}

Thus number of stamps with penny in terms of x is \frac{x}{6}

7 0
3 years ago
Value of the y-intercept of the graph of f(x) = e1–x – 1?
frozen [14]

Answer:

(0, e-1) or (0, 1.718) to the nearest thousandth.

Step-by-step explanation:

The y-intercept occurs when x = 0 so here we have:

y = e^(1 - 0) - 1

= e - 1

So the y-intercept is the point (0, e-1)

5 0
3 years ago
-2+4(-x+4)=10 using distributive property and collecting like terms
stich3 [128]

Answer:

<h2>x = 1</h2>

Step-by-step explanation:

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4 0
3 years ago
If two distinct planes intersect , then their intersection is a line . Which geometry term does the statement represent
Rom4ik [11]

Answer:

POSTULATE

Step-by-step explanation:

<em>A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven </em>

<em> </em>

<em>  </em>

<em> </em>

<em>In geometry, the theorem is considered valid or correct with which its assertion is practically not refuted by almost anyone, whether it is really true or not. </em>

<em> </em>

<em>  </em>

<em> </em>

<em>This, in practice, implies that all students of the subject share the same criteria on the theory. Thus, the postulates, in short, have the following characteristics: </em>

<em> </em>

<em>  They are presumed true by most of the scholars in the field. </em>

<em> </em>

<em>Its contradiction goes against the very essence of the subject. </em>

<em> </em>

<em>Postulate 6: If two planes intersect, then their intersection is a line.</em>

<em />

<em>See Attachment for Details ^^</em>

<em>The image attached  represents the statement given in the question (If two distinct planes intersect, then their intersection is a line)</em>

<em>Therefore</em><em>, </em>

<em> </em>

<em>The Geometry term that represents the statement above is POSTULATE</em>

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2 years ago
You are in a bike race. When you get to the first checkpoint, you are $\frac{2}{5}$
Black_prince [1.1K]

Answer:

The distance from the star to the second checkpoint is 4 miles

Step-by-step explanation:

The complete question in the attached figure

we know that

When you get to the second checkpoint, you are 1/4 of the distance to the finish

so

The distance from the star to the second checkpoint is equal to the total distance multiplied by 1/4

The total distance is 40 miles ( see the attached figure)

so

The distance from the star to the second checkpoint is

\frac{1}{4}(40)=10\ miles

<em>Find out the distance from the start to the first checkpoint</em>

Multiply the distance from the star to the second checkpoint by 2/5

\frac{2}{5}(10)=4\ miles

6 0
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