All categories

2 years ago

Find the exact value of cos 15°

Mathematics

2 answers:

Reil [10]2 years ago

5 0

Answer:

$\frac{\sqrt{6}+\sqrt{2} }{4}$

Step-by-step explanation:

Using the difference formula for cosine and the exact values

cos45° = sin45° = $\frac{\sqrt{2} }{2}$ , cos30° = $\frac{\sqrt{3} }{2}$ , sin30° = $\frac{1}{2}$

cos(a - b) = cosacosb + sinasinb

Note 15° = 45° - 30°, thus

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= ( $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ ) + ( $\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$ )

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}+\sqrt{2} }{4}$

Zielflug [23.3K]2 years ago

3 0

Answer:

$\frac{\sqrt{6} +\sqrt{2} }{4}$

Step-by-step explanation:

You might be interested in

7x31=????????????????

Hunter-Best [27]

Answer:

217

Step-by-step explanation:

7 × 31 = 217

I hope this helps!

8 0

2 years ago

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Leona [35]

Answer:

1 and 4 are correct. 2 and 3 are not.

Step-by-step explanation:

When x = 0 where does the horse start?

y = 1.5*sin(0 + 0.5)*2*pi + 1.5

y = 1.5*sin(0.5*2pi) + 1.5

y = 1.5*sin(pi) + 1.5 But sin pi = 0

y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.

This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.

You can figure this one out by letting x = 0.01 When it does then the value of the function is

y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5

y = 1.5*sin(0.51*2*pi) + 1.5

y = 1.5*sin(3.204424) + 1.5

y = 1.5*(- .0623) + 1.5

y = -0.9418 + 1.5

y = 1.4058 so it is going downward The value is getting smaller.

The horse starts out in the middle of the pole. What does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)

That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.

6 0

3 years ago

The sum of three numbers is 110. The third number is 3 times the first. The second number is 5 more than the first. What are the

g100num [7]

Answer:

The numbers are 63, 26, & 21

Step-by-step explanation:

110 = 3x + (5 + x) + x

105 = 3x + 2x

105 = 5x

21 = x

Plug it back into the first equation to find your values

6 0

2 years ago

A chemical company makes two brands of antifreeze the first brand contains 65% pure antifreeze and the second brand contains 80%

liq [111]

Answer:

30 gallons of each brand

Step-by-step explanation:

1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)

8 0

2 years ago

What are the solutions of the quadratic equation 49x^2=9?

Flauer [41]

<span>Simplifying 49x^2 + -9 = 0
Reorder the terms: -9 + 49x^2 = 0
Solving -9 + 49x^2 = 0 Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation. -9 + 9 + 49x^2 = 0 + 9
Combine like terms: -9 + 9 = 0 0 + 49x^2 = 0 + 9 49x^2 = 0 + 9
Combine like terms: 0 + 9 = 9 49x^2 = 9
Divide each side by '49'. x^2 = 0.1836734694
Simplifying x^2 = 0.1836734694
Take the square root of each side: x = {-0.428571429, 0.428571429}

hope this helps!!</span>

5 0

2 years ago