All categories

2 years ago

Find the exact value for cos π 12 applying sum and difference formulas involving π 3 and π 4 .

1 answer:

8 0

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split into π/3−π/4.

cos(π/3−π/4)

Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/3) is 12, so:

(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/4) is √22.

(12)⋅(√22)+sin(π/3)⋅sin(π/4)

The exact value of sin(π/3) is √32.

(12)⋅(√22)+(√32)⋅sin(π/4)

The exact value of sin(π/4) is √22.

(12)⋅(√22)+(√32)⋅(√22)

Simplify each term:

√24+√64

Combine the numerators over the common denominator.

You might be interested in

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

FromTheMoon [43]

Answer:

Here is the question attached with.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ is a straight line.

$\angle AEF$ is a right angled triangle.

Options $1,4,5,6$ are correct answers.

Step-by-step explanation:

⇒As $\ ray\ AE$ is ⊥ $FEC$ so it will forms right angled triangle then $m\angle CEA =90\ (deg)$ .

⇒Measure of $\angle BEF =135\ (deg)$ as $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ is the bisector of $\angle AEC$ ,meaning that $\angle AEB$ is half of $\angle AEC$ so $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ is a straight line as the angles measure over it is $180\ (deg)$ .

⇒Measure of $\angle AEF = 90\ (deg)$ from linear pair concept.

As $\angle CEA + \angle AEF = 180\ (deg)$ ,plugging the values of $m\angle CEA =90\ (deg)$ we have $\angle AEF = 90\ (deg)$ .

The other two options are false as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it is exceeding $180\ (deg)$ whereas $\angle CEF$ is a

straight line.

And $m\angle CEB=2(m\angle CEA)$ is not true.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

So we have total $4$ answers.

The correct options are $1,4,5,6$ .

5 0

2 years ago

Read 2 more answers

An engineer is designing an arch-shaped gate for the entrance to an amusement park. The gate must be 80 feet wide and 25 feet ta

Tom [10]

1) the form of the equation may be written as y = A(X - Xo)(X - X1)

Where Xo and X1 are the two roots of the equation.

2) We can fix the system of coordinates so that the vertex is in the middle of the gate => Xo = - 40 and X1 = +40

=> y = A (X + 40) (X - 40) = A (X^2 - 1600)

3) The height, at X = 0 is 25

=> A(0 - 1600) = 25

=> -1600A = 25 => A = -25 / 1600 = - 1/64

4) The equation is y = - [1/64] (X^2 - 1600)

5) You can present it in different equivalent forms.

Some of those other forms are:

1) - 64y = (x^2 - 1600)

2) x^2 = - 64y + 1600

3) X^2 = - 64 (y - 25)

4 0

1 year ago

City planners are creating a 3-dimensional model of a city park to find the best placement for a new tennis court. The city park

inn [45]

First, divide the original measurements with the scaled ones. You'll get the same answer meaning that is the scale used by the model.
1500 ft. ÷7.5 ft = 200
600 ft. ÷ 3 ft. = 200

To simply check, if you divide 1500 with 200, the answer is 7.5 and 600 divided by 200 is 3.
To find the scaled dimension of the tennis court with actual dimension of 120 ft by 60 ft, divide both values with the scale used in the model which is 200.

120 ft. ÷ 200 = 0.6 ft
60 ft. ÷ 200 = 0.3 ft

The dimension of the tennis court in the scaled model is 0.6 ft long and 0.3 ft. wide.

8 0

1 year ago

32.15 is written correctly in EXPANDED FORM using FRACTIONS

marshall27 [118]

Answer:

Step-by-step explanation:

: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5 0

1 year ago

In ΔVWX, x = 5.3 inches, w = 7.3 inches and ∠W=37°. Find all possible values of ∠X, to the nearest 10th of a degree.

STALIN [3.7K]

Answer:

que?

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers