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olasank [31]
3 years ago
10

The angle addition postulate is sometimes described as "the whole is equal to the sum of its parts." Explain how this descriptio

n applies to the angle addition postulate.

Mathematics
1 answer:
Vsevolod [243]3 years ago
5 0
To explain this clearly, refer to the figure attached. 

Angle addition, from the name itself, is the sum of the smaller angles to make up the bigger angle. In that case, the yellow angle plus the green angle, equals the maroon angle. As long as they have the same vertex (vertex O), you can add up angles that are side by side to obtain the value of the total angle. That is what the phrase <span>"the whole is equal to the sum of its parts" means.</span>

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Prove the identity.
Delvig [45]

Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

5 0
3 years ago
PLEASE HELP!!!<br> Find the common difference for the arithmetic sequence. -55, -50, -45, -40.....
Fed [463]

Answer:

5

Step-by-step explanation:

Just grap any two consecutive terms in the sequence. lets say -55 and -50

-50-(-55) = 5

you can check this by picking two other terms

7 0
2 years ago
Samantha sends her son, Barry, to a preschool center on certain days. The cost of preschool is $45 per day along with a fixed mo
Hatshy [7]

Answer: Option D

D. 880 = 45d + 70; 18 days

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call d the number of days that Barry attends school

So the cost was:

45d + 70 = 880

Now we solve the equation for the variable d

45d= 880-70

45d= 810

d= \frac{810}{45}

d= 18\ days

The answer is the option D

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3 years ago
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Sauron [17]
(17-7)*2=weekly allowance
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