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zmey [24]
3 years ago
15

If sin Θ = 2 over 3 and tan Θ < 0, what is the value of cos Θ?

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0
Sinθ = (2/3)    tanθ < 0  Implies tanθ = Negative.

For sin positive and tan negative, implies θ is in the second quadrant.

<span>Sinθ = (2/3) = opposite / Hypotenuse.

Adjacent side:

x</span>² + 2² = 3²

x² + 4 = 9<span>

</span>x<span>² = 9 - 4
</span>
x<span>² = 5
</span><span>
x = </span>√5 = Adjacent.
<span>
cos</span>θ  =  Adjacent / Hypotenuse =  √5 / 3
<span>
Since </span><span>θ is in the second quadrant, cosine is also negative in the second quadrant.
</span><span>

Therefore:

</span>cos<span>θ  =  - (√5/3)
</span>
The last option from the top :  <span>negative square root of 5 over 3</span>
You might be interested in
Horizontal translation
vampirchik [111]

Answer:

The correct option is;

Reflection over the y-axis

Step-by-step explanation:

An even function is a function that satisfies the following function equation;

f(x) = f(-x)

Therefore, for an even function, we have;

f(x) - f(-x) = 0

Which gives that the values of f(x) of the even function is the same upon reflection about the y-axis whereby the values of x changes from x to -x

Therefore, the symmetry of an even function is about the y-axis

However, an odd function is a function that satisfies the following function equation;

f(-x) = -f(x)

Therefore, reflection across the y-axis will result in an inversion of the odd function such that the odd function is not symmetrical about the y-axis as we have;

f(-x) = -f(x) ≠ f(x) which simplifies to f(x) ≠ f(-x).

5 0
4 years ago
Anybody know this question
Dmitrij [34]
<h3>Answers :-</h3>
  • sinB = 12/13
  • cosB = 5/13
  • tanB = 12/5

Here as by the given information ,

♦ sinA = Opposite/Hypotenuse

♦ cosA = Adjacent/Hypotenuse

♦ TanA = Opposite/adjacent

So here we need to find the same for angle B so we need to use the same formulas for angle B also .

→ sinB = Opposite/Hypotenuse = 12/13

→ cosB = Adjacent/Hypotenuse = 5/13

→ tanB = Opposite/Adjacent = 12/5

8 0
3 years ago
The angle measures of a triangle are 2x+5 degrees 6x-5 degrees and 7x degrees. What is the value of x?
pav-90 [236]

Answer:

x = 12

Step-by-step explanation:

We know that the total angle measure of a triangle is 180 degrees, so the sum  of all the angles should be 180 degrees.

Therefore, we can add all the angles, set them equal to 180 and solve for x

2x+5 + 6x-5 + 7x = 180

We can combine all the x terms and all the numerical terms on the left side of the equation to get:

(2x+6x+7x) + (5-5) = 180

15x = 180

Then we can divide both sides by 15 to isiolate x

15x = 180

x = 180/15 = 12

6 0
3 years ago
11. The Leonin family used 90 kWh for their electric consumption for the month of
almond37 [142]

Answer:

The electric bill of the Leonin family was of $ 877,626.

Step-by-step explanation:

Given that the Leonin family used 90 kWh for their electric consumption for the month of August, if the power consumption costs P9.7514 per kWh, to determine how much is their electric bill, the following calculation must be performed:

9.7514 x 90 = X

877.626 = X

Thus, the electric bill of the Leonin family was of $ 877.626.

3 0
3 years ago
the temperature is already at 40 degrees it rises 4.5 degrees per minute how long will it take to get to 76 degrees​
Andrei [34K]

Answer:

It will take 8 minutes for the temperature to reach 76°

Step-by-step explanation:

The expression for the total temperature in degrees at time t can be written as;

T=I+EM

where;

T=total temperature

I=initial temperature

E=temperature increase per minute

M=number of minutes

This can also be written as;

total temperature=initial temperature+temperature increase per minute×number of minutes

In our case;

T=76°

I=40°

E=4.5°

M=m

replacing;

76=40+(4.5×m)

4.5 m=76-40=36

(4.5 m)/4.5=36/4.5

m=8

It will take 8 minutes for the temperature to reach 76°

7 0
4 years ago
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