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erastova [34]
2 years ago
9

Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i

Mathematics
1 answer:
Nataliya [291]2 years ago
7 0

The solution to given expression tan(2θ) is 22.615°

For given question,

We have been given an expression tan(2θ)

Given that cos(θ) = 5/13, and θ is in quadrant 1.

We know that the trigonometric identity

sin²θ + cos²θ = 1

⇒ cos²θ = (5/13)²

⇒ sin²θ = 1 - 25/169

⇒ sin²θ = 169 - (25/169)

⇒ sin²θ = 144/169

⇒ sin(θ) = 12/13

We know that the identity cos(2x) = cos²x - sin²x

⇒ cos(2θ) = cos²θ - sin²θ

⇒ cos(2θ) = 25/169 - 144/169

⇒ cos(2θ) = -119/169

And sin(2x) = 2sin(x)cos(x)

⇒ sin(2θ) = 2sin(θ)cos(θ)

⇒ sin(2θ) = 2 × 12/13 × 5/13

⇒ sin(2θ) = 120/169

We know that, tan(x) = sin(x)/cos(x)

⇒ tan(2θ) = sin(2θ)/cos(2θ)

⇒ tan(2θ) = (120/169) / (-119/169)

⇒ tan(2θ) = 120 / (-119)

⇒ tan(2θ) = -1.008

Since θ is in quadrant 1, tan(2θ) = 1.008

⇒ 2θ = arctan(1.008)

⇒ 2θ = 45.23

⇒ θ = 22.615°

Therefore, the solution to given expression tan(2θ) is 22.615°

Learn more about the expression here:

brainly.com/question/14961928

#SPJ4

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ValentinkaMS [17]

By using the concept of uniform rectilinear motion, the distance surplus of the average race car is equal to 3 / 4 miles. (Right choice: A)

<h3>How many more distance does the average race car travels than the average consumer car?</h3>

In accordance with the statement, both the average consumer car and the average race car travel at constant speed (v), in miles per hour. The distance traveled by the vehicle (s), in miles, is equal to the product of the speed and time (t), in hours. The distance surplus (s'), in miles, done by the average race car is determined by the following expression:

s' = (v' - v) · t

Where:

  • v' - Speed of the average race car, in miles per hour.
  • v - Speed of the average consumer car, in miles per hour.
  • t - Time, in hours.

Please notice that a hour equal 3600 seconds. If we know that v' = 210 mi / h, v = 120 mi / h and t = 30 / 3600 h, then the distance surplus of the average race car is:

s' = (210 - 120) · (30 / 3600)

s' = 3 / 4 mi

The distance surplus of the average race car is equal to 3 / 4 miles.

To learn more on uniform rectilinear motion: brainly.com/question/10153269

#SPJ1

4 0
1 year ago
Are these triangles congruent? If so, state the rule which you used to determine congruence
Zepler [3.9K]

Answer:

not necessarily confident cuz simply it doesn't look same size it should be similar

3 0
3 years ago
In a​ survey, the eye colorseye colors of respondents are identified as 11 for brown eyes commabrown eyes, 22 for blue eyes comm
mr Goodwill [35]

Answer:

The answer is ratio Level of measurement

Step-by-step explanation:

It is important that I explain the various levels of measurement. There are four levels of measurement;  nominal, ordinal, interval and ratio levels of measurement.

1. Nominal Level of Measurement;  The nominal scale or level of measurement simply names or categorizes responses. examples are categorizing entries into religion, gender, hair color, etc. It is the lowest scale of measurement and they do not imply ordering among the group example, in classifying hair color, there is no numerical ordering value or red being more than black.

2. Ordinal Level of Measurement; Ordinal scale allows for comparison between two subjects to the degree of which they posses the dependent variable. For example, a researcher wanting to determine the level of satisfaction of customers to a product can group the customers from most dissatisfied to most satisfied.

3. Interval Level of Measurement; here, the level of measurement are numerical and they have the same distance (degree of difference) throughout. In the interval level of measurement, there is no true zero point on the scale, but the distance between two sets of points can have the same interval, but it will be irrational to make ratio comparisons. example is the Fahrenheit scale for temperature measurement, there is no true zero point, but a temperature difference between 20° F and 30° F is the same as the difference between 50° F and 60° F.

4. Ratio Level of Measurement; This is the most detailed level of measurement, and in addition to the interval scale, there is a true zero point. Mathematical computations can be carried out on them. It can be said to be the other three levels of measurement summed up in one. For example, money can be measured on the ratio scale because there is a zero point and it is mathematically accurate to say that 20 cents is twice as much as 10 cents. In our example, the survey is on eye color which ordinarily would have been on the nominal or categorical scale of measurement, but for the fact that the number of people possessing a quality is counted, it makes it ratio, and mean value was even calculated to be 1.5. There is a possibility of having a particular group of eye color with no participant, hence the zero point.

3 0
3 years ago
What is the equation of this line?
Margarita [4]

Answer: either b or c

Step-by-step explanation:

¸.•´*¨`*•✿ ✧・゚: *✧・゚:* Jax *:・゚✧*:・゚✧✯✿•*`¨*`•.¸✯

3 0
3 years ago
What is an equation of the line that is parallel to y=3x-8 and passes through the point (4,-5)
Anna [14]
Pareallell lines have same slope
y=mx+b, m=slope
y=3x-8 so we need
y=3x+b
find b

so given (4,-5)
we can subsitute the point
(x,y)
(4,-5)
x=4 then y=-5

so
-5=3(4)+b
-5=12+b
-17=b


y=3x-17 is equation
D is answer
3 0
3 years ago
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