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.
<span>(√2+√6)
/ 4</span>
Initial repair cost = $1200
Gratuity = 15% of the initial repair cost
= 15% of 1200
= 15 × 12
= 180
Hence, the gratuity for the service is $180.
<h2>
Area of rectangular board is 1920000 square millimeters</h2>
Step-by-step explanation:
A rectangular board is 1.6 meters long and 1.2 meters wide.
Here we need to find the area of the board in square millimeters.
Length = 1.6 m= 1.6 x 1000 = 1600 mm
Width = 1.2 m= 1.2 x 1000 = 1200 mm
Area = Length x Width
Area = 1600 x 1200
Area = 1920000 square millimeters
Area of rectangular board is 1920000 square millimeters
You have the following expression given in the problem:
f(x) = x³ – 2x²<span> – x + 2
Therefore, to find the roots, you must apply the proccedure shown below:
1. You have:
0 </span><span>= x3 – 2x2 – x + 2
2. Then, when you factor, you obtain:
(x-2)(x-1)(x+1)=0
3. Therefore, you have that the roots are the following:
x1=-1
x2=1
x3=2</span>
<span>The question asks us to determine the values for a and b in the linear equation. Linear equation in the slope-intercept form is : y = a x + b. This equation is: y = 2.25 x - 3.15. The slope: a = 2.25 and the y-intercept is: b = -3.15. Answer: a = 2.25 and b = - 3.15.</span>
