MATHEMATICS COLLEGE

The expression cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5 can be rewritten as which of the following? cosine of 7 times pi over 10
cosine of 3 times pi over 10
sine of 7 times pi over 10
sine of 3 times pi over 10

(The clear version of the question is in the picture below)

Answers

Answer 1

Answer:

Answer:

(b) cos(3π/10)

Step-by-step explanation:

The given expression matches the trig identity form for the cosine of the difference of two angles:

cos(α-β) = cos(α)cos(β) +sin(α)sin(β)

To match the given expression exactly, we can choose ...

α = π/2

β = π/5

Then the difference is ...

α -β = π/2 -π/5 = (5/10)π -(2/10)π = 3π/10

The given expression can be shortened to ...

cos(3π/10)

Additional comment

Sometimes it can be difficult to remember when the signs in trig identities match, and when they differ. The fact that cosines of smaller angles have larger values can be a peg on which to hang that hat.

Answer 2

Answer:

Final answer:

The expression 'cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5'' can be rewritten as 'cosine of 3 times pi over 10' by using the cosine addition formula.

Explanation:

The question is related to the usage of trigonometric identities and laws, specifically the cosine addition formula. This formula is defined as: cos(a + b) = cos a cos b - sin a sin b. Looking at your original expression, we can identify a and b based on this definition, to make it align with the cosine addition formula structure. Let's pick a = pi/2 and b = pi/5.

Therefore, your original equation can be transformed as follows:

cos(pi/2)cos(pi/5) + sin(pi/2)sin(pi/5) = cos((pi/2) - (pi/5)) = cos(3pi/10).

So, the expression 'cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5' can be rewritten as 'cosine of 3 times pi over 10.' We have used the cosine addition formula to simplify the original expression.

Learn more about Cosine Addition Formula here:

brainly.com/question/36770188

#SPJ3

Related Questions

A shipping container will be used to transport several 60-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 26000 kilograms. Other shipments weighing 13200 kilograms have already been loaded into the container. What is the greatest number of 60-kilogram crates that can be loaded into the shipping container?
Can someone help me out this is hard
Find the distance between the point (-18,-19) and the point (-18,16).
What is the square root of 64y16?o 44O 4yo 8o gy
Its due soon help ill give brainliestThe price of a pair of headphones at Store A is 3/4 the price at Store B.The price at Store A is $89.25. Find how much you save by buying the headphones at Store Aa. 119b. 72c. 29.75

How many different patrols of 6 girls can be selected from a troop of 24 Girl Scouts?

Answers

Answer:

Step-by-step explanation:

A coral reef grows 0.14 m every week. How much does it grow in 14 weeks? Write your answer in millimeters.

Answers

Answer:

0.14*14= 1.96

Step-by-step explanation:

Must multiply 0.14 times 14 for the answer.

An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=103+30x. Predict the weight of luggage for a flight with 86 passengers.

Answers

Answer:

2683

Step-by-step explanation:

Using the linear regression equation that predict the relationship between the weight of the luggage and the total number of passenger y = 103 + 30x, we can plug in the number of passenger x = 86 to predict the weight of the luggage on a flight:

y = 103 + 30*86 = 2683

2. The path of a high diver is given by y = + (2x2 – 9x – 56), where y is the height of the diverabove the water and x is the horizontal distance from the diving board (in feet). How far from the
end of the diving board is the diver when he hits the water?

Answers

Answer:

The diver will be 8 feet from the end of the board when he hits the water.

Step-by-step explanation:

The diver hits the water when y = 0.

To find the distance, we have to find the values of x when y = 0.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^(2) + bx + c, a\neq0$ .

This polynomial has roots $x_(1), x_(2)$ such that $ax^(2) + bx + c = (x - x_(1))*(x - x_(2))$ , given by the following formulas:

$x_(1) = (-b + √(\bigtriangleup))/(2*a)$

$x_(2) = (-b - √(\bigtriangleup))/(2*a)$

$\bigtriangleup = b^(2) - 4ac$

In this problem, we have that:

$y = 2x^(2) - 9x - 56$

$2x^(2) - 9x - 56 = 0$

$a = 2, b = -9, c = -56$

Then

$\bigtriangleup = b^(2) - 4ac = (-9)^(2) - 4*2(-56) = 529$

$x_(1) = (-(-9) + √(529))/(2*2) = 8$

$x_(2) = (-(-9) - √(529))/(2*2) = -3.5$

It is a horizontal distance, so the answer is a positive value.

The diver will be 8 feet from the end of the board when he hits the water.

Limit of x^2-81/x+9
As x goes toward -9

Answers

Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18

Help? Question are above. 15 points