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enot [183]
3 years ago
15

Given that tan θ ≈ −0.087, where 3 2 π < θ < 2 , π find the values of sin θ and cos θ.

Mathematics
1 answer:
elena-s [515]3 years ago
4 0

Answer:

  • sin θ ≈ -0.08667
  • cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

  sin(-0.08678 radians) ≈ -0.08667

  cos(-0.08678 radians) ≈ 0.99624

_____

<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

  \cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

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What is the qoutient of 1/6 and 2/9
beks73 [17]

Answer:

\frac{3}{4}

Step-by-step explanation:

To find the quotient, we first need to know what quotient means.

Quotient is the solution to division problems.

So here is how we have to do this, first we identify our fractions:

\frac{1}{6}   and    \frac{2}{9}

Next, we must turn the fraction we are dividing by into a reciprocate:

\frac{2}{9} turns into \frac{9}{2}

Now we have \frac{1}{6} and \frac{9}{2}

Next, we multiply!:

\frac{1}{6} x \frac{9}{2} = \frac{9}{12}

Simplified:

\frac{3}{4}

8 0
3 years ago
Read 2 more answers
Kelsey graphed the equation y = 3x + 1 as shown below.
USPshnik [31]

Answer:

D. Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.

Step-by-step explanation:

The equation to graph was : y= 3x + 1 where the slope is 3 and the y-intercept is 1

However, Kelsey graph line passes through points (-3, 0)and (0, 3).From these points the equation of the line is;

m=Δy/Δx  where

m=the slope of the graph

Δy= 3-0 =3

Δx= 0--3 =3

m=3/3 = 1

The equation of the line should be;

m=Δy/Δx

1=y-3/x-0

1x= y-3

3+1x= y

y= 1x + 3 ----------where the slope is 1 and y-intercept is 3

So you can see here that in the original equation,<em> the slope m is 3 and y-intercept is 1 as shown in the first attached graph.</em>

While in the Kelsey's graph, <em>the slope is 1 and the y-intercept is 3 as in the second attached graph. </em>

<em>Thus, the correct answer is D : Kelsey graphed </em><u><em>the slope,3</em></u><em> as the </em><em>y-intercept </em><em>and the</em><u><em> y-intercept,1,</em></u><em> as the slope. </em>

Answer choice A is incorrect because Kelsey didnot graph the y-intercept, 1 on the x-axis but graphed point (-3,0) on the x-axis.

Answer choice B is incorrect because on Kelsey's equation the y-intercept is 3 and not -3. i.e. y=1x + 3

Answer choice C is incorrect because Kelsey graphed the slope as up 1 right 1 which is okay per the equation , y=1x+3.However, this incorrect because the correct graph has a slope of 3.

4 0
3 years ago
Read 2 more answers
Write 42/100 in standard form as a decimal
iragen [17]

Answer:

0.42

Step-by-step explanation:

divide 100÷42 then the answer is 0.42

3 0
3 years ago
What is the value of x?
Agata [3.3K]

Answer:

x=68

Step-by-step explanation:

We begin by setting up as a proportion. 99.2 and 112 ft are across from each other so we can put those as our numerators. Additionally 62 and (x+2) ft are across from each other so we can put those as denominators. Now we can set up our proportion and begin to cross multiply:

99.2/62 = 112/(x+2) is our equation. It might help you see it clearly to write it out as fractions. From here, we cross multiply.

When we do that, we get x=68

3 0
2 years ago
Which of the following is a statistical question
zmey [24]

Answer:

its d because who askes that question

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2 years ago
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