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3 years ago

Use the sum and difference identities to find the exact values of the sine, cosine, and tangent of the angle. . 165 = 135 + 30

1 answer:

4 0

So lets get to the problem

165°= 135° +30° 

To make it easier I'm going to write the same thing like this 
165°= 90° + 45°+30° 

Sin165° 
= Sin ( 90° + 45°+30° ) 
= Cos( 45°+30° )..... (∵ Sin(90 + θ)=cosθ 
= Cos45°Cos30° - Sin45°Sin30° 

Cos165° 
= Cos ( 90° + 45°+30° ) 
= -Sin( 45°+30° )..... (∵Cos(90 + θ)=-Sinθ 
= Sin45°Cos30° + Cos45°Sin30° 

Tan165° 
= Tan ( 90° + 45°+30° ) 
= -Cot( 45°+30° )..... (∵Cot(90 + θ)=-Tanθ 
= -1/tan(45°+30°) 
= -[1-tan45°.Tan30°]/[tan45°+Tan30°] 

Substitute the above values with the following... These should be memorized 
Sin 30° = 1/2 
Cos 30° =[Sqrt(3)]/2 
Tan 30° = 1/[Sqrt(3)] 
Sin45°=Cos45°=1/[Sqrt(2)] 
Tan 45° = 1

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Face north. do a 1/4 turn clockwise which way will i be facing

Alla [95]

Answer:

You will be facing in a 90 degree angle.

Step-by-step explanation:

Did you mean like on a compass?

5 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Csf%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Ccfrac%7B%5Csqrt%7Bx-1%7D-2x%20%7D%7Bx-7%7D" id=

BARSIC [14]

<h3>Answer: -2</h3>

======================================================

Work Shown:

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}\left(\sqrt{x-1}-2x\right) }{ \frac{1}{x}\left(x-7\right) }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}*\sqrt{x-1}-\frac{1}{x}*2x }{ \frac{1}{x}*x-\frac{1}{x}*7 }\\\\\\$

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}}*\sqrt{x-1}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}*(x-1)}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x}-\frac{1}{x^2}}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \frac{ \sqrt{0-0}-2 }{ 1-0 }\\\\\\\displaystyle L = \frac{-2}{1}\\\\\\\displaystyle L = -2\\\\\\$

-------------------

Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

I'm using the rule that

$\displaystyle \lim_{x\to\infty} \frac{1}{x^k} = 0\\\\\\$

where k is some positive real number constant.

Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.

In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

This effectively means,

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 } = \lim_{x\to\infty} \frac{ -2x }{ x} = -2\\\\\\$

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

5 0

2 years ago

What are two solutions of 3 + 4 |x/2 + 3| = 11?

Alex

3 + 4abs(x/2 + 3) = 11 Subtract 3
4 abs(x/2 + 3) = 11 - 3
4 abs(x/2 + 3) = 8 Divide by 4
abs(x/2 + 3) = 8/4
abs(x/2 + 3) = 2

Solution 1
x/2 + 3 = 2 Subtract 3
x/2 = 2 - 3
x/2 = - 1 Multiply by 2
x/2 *2 = - 2
x = - 2

Solution 2
x/2 + 3 = - 2
x/2 = - 2 - 3
x/2 = - 5 Multiply by 2
x = -5 * 2
x = -10

Solutions
x = - 2 <<<< answer 1
x = -10 <<<< answer 2

3 0

3 years ago

Can someone help me pls thanks

patriot [66]

If 4600 corresponds with 100, multiply 4600 by .09 and you get 414.

Also:

46 * 9 = 414

5 0

3 years ago

Ow to do this please help I’m 10in six grade I skip don’t no why but please help

ohaa [14]

To do this, you can just multiply across. 3 times 1 equals 3 so your numerator is 3. 2 times 4 equals 8. Then, your answer would be 3/8. Hope this helps :)

4 0

3 years ago

Read 2 more answers