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

There are 8 sophomores on the academic team. At the last competition, they each took the math test. Their scores were 82%, 92%,

Sav [38]

Answer:

79%

Step-by-step explanation:

To find the median, you need to arrange the numbers in ascending order. Than pick the middle number. If there are two middle numbers then you add them together and then divide by 2.

3 0

2 years ago

1.488 divided by 2.1 rounded to nearest tenth

Neko [114]

The answer should be 0.70

7 0

2 years ago

A cube-shaped water tank having 6 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tan

Mekhanik [1.2K]

Answer:

0.033 ft

Step-by-step explanation:

Let g = 32.2 ft/s2 and h be the maximum height that water can be filled before the sides shatter.

Pressure is distributed from 0 to maximum at the bottom like the following equation:

$P = \rho gh$

So the force generated by water pressure on the side of the tank is

$F = PA = \rho ghs/2$

where s = 6ft is the side length of the tank. This force cannot be larger than 200lb

$\rho ghs/2 \leq 200$

$62.4*32.2*h*6/2 \leq 200$

$h \leq 0.033 ft$

4 0

2 years ago

Rational number 3 by 40 is equals to

kkurt [141]

Answer:

6/80, 9/120, 12/160 etc

8 0

2 years ago

Read 2 more answers

Which shows the correct first step to solving the system of equations in the most efficient manner? 3 x + 2 y = 17. x + 4 y = 19

skelet666 [1.2K]

Answer: First option.

Step-by-step explanation:

<h3> The missing picture is attached.</h3><h3></h3>

You can use these methods to solve a System of Equations and find the value of the variables:

A. Substitution method.

B. Elimination method.

In this case, given the following System of equations:

$\left \{ {{3 x + 2 y = 17} \atop {x + 4 y = 19}} \right.$

The most efficient method to solve it is the Substitution Method. The procedure is:

Step 1: Solve for one of the variables from the most convenient equation.

Step 2: Make the substitution into the other equation and solve for the other variable in order to find its value.

Step 3: Substitute the value obtained into the equation from Step 1 and evaluate, in order to find the value of the other variable.

Based on this, you can identify that first step to solve the given System of equations, is solving for "x" from the second equation:

$x + 4 y = 19\\\\x=-4y+19$

3 0

2 years ago

Read 2 more answers