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geniusboy [140]

4 years ago

14

Verify the identity. sin (x+pi/2)=cos x

1 answer:

hram777 [196]4 years ago

4 0

Given data
<span>sin (x+pi/2)=cos x
</span>now using sin law
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
now using above values
sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x)
as we know that
sin(pi/2)=1
cos(pi/2)=0
now putting these values
sin(pi/2+x)=1*cosx+0*1
sin(pi/2+x)=cosx
hence proved that

<span>sin (x+pi/2)=cos x</span>

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Write an equation of the line containing the point (6,-4) and perpendicular to.the line y=-2x-3

igor_vitrenko [27]

Answer:

$y=\frac{1}{2}x-7$

Step-by-step explanation:

So we need to find an equation of a line that crosses the point (6,-4) and is perpendicular to y = -2x -3.

First, let's find the slope of the line we want to write. The line we want is perpendicular to y = -2x -3. Recall that if two lines are perpendicular to each other, their slopes are negative reciprocals of each other. What this means is that:

$m_1\cdot m_2=-1$

Plug -2 for one of the slopes.

$-2\cdot m_2=-1$

Divide by -2 to find the slope of our line.

$m_2=1/2$

Thus, our line needs to have a slope of 1/2.

Now, let's use the point-slope form. The point-slope form is given by:

$y-y_1=m(x-x_1)\\$

Plug in 1/2 for the slope m and let's let our point (6,-4) be x₁ and y₁. Thus:

$y-(-4)=\frac{1}{2}(x-6)\\$

Simplify and distribute:

$y+4=\frac{1}{2} x-3$

Subtract 4 from both sides:

$y=\frac{1}{2}x-7$

The above is the equation that passes the point (6,-4) and is perpendicular to y = -2x -3.

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Mnenie [13.5K]

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Step-by-step explanation:

The interquartile range is the range within the boxed areaa. You subtract the minimum value from the maximum value.

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