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Marat540 [252]
3 years ago
5

Number 12 pleaseeeee

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

Hey there!

Here is your inequality -

\frac{-x}{4} \leq 1

The first thing you need to do is cross multiply -

-x \leq 4 \times 1 \\ \\ -x\leq 4

Your inequality has to be positive. Divide both sides by -1 to cancel out the negative sign -

\frac{-x}{-1} \leq \frac{4}{-1} \\ \\ x\geq -4

The sign changes when the variable is negative.

Hope this helps! :)

Also, here is the graph -

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A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t
Ivan

Answer:

sin t = \frac{3}{5}

cos t = -\frac{4}{5}

tan t = -\frac{3}{4}

csc t = \frac{5}{3}  

sec t = -\frac{5}{4}  

cot t = -\frac{4}{3}  

Step-by-step explanation:

In the unit circle:

  • x-coordinate of a point on the circle represents cosine the angle between the + ve part of x-axis and the terminal side which joins the center of the circle and this point
  • y-coordinate of a point on the circle represents sine the angle between + ve part of x-axis and the terminal side which joins the center of the circle and this point

In the attached figure

∵ t represents the angle between + ve part of x-axis

    and the terminal side drawn from the center of the circle to

    point P

∴ The coordinates of point P are (cos t , sin t)

∵ The coordinates of P are ( -\frac{4}{5} , \frac{3}{5} )

∴ sin t = \frac{3}{5}

∴ cos t = -\frac{4}{5}

∵ tan t = \frac{sin(t)}{cos(t)}

- Substitute the values of sin t and cos t

∴ tan t = \frac{\frac{3}{5}}{-\frac{4}{5}}

- Multiply up and down by 5 to simplify the fraction

∴ tan t = -\frac{3}{4}

∵ csc t = \frac{1}{sin(t)}

- Reciprocal the value of sin t

∴ csc t = \frac{5}{3}  

∵ sec t = \frac{1}{cos(t)}

- Reciprocal the value of cos t

∴ sec t = -\frac{5}{4}  

∵ cot t = \frac{1}{tan(t)}

- Reciprocal the value of tan t

∴ cot t = -\frac{4}{3}  

3 0
4 years ago
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