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3 years ago

9 points

Mathematics

1 answer:

s2008m [1.1K]3 years ago

6 0

Answer:

$3.21

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

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Given cos theta = - 2/5 and sin theta < 0, find the six trigonometric values. I need help with this

Lena [83]

Answer:

$\sin\,\theta =-\frac{\sqrt{21} }{5}$

$\tan\,\theta =\frac{\sqrt{21} }{2}$

$\sec\,\theta = \frac{-5}{2}$

$cosec\,\theta =\frac{-5}{\sqrt{21} }$

$\cot\,\theta =\frac{2}{\sqrt{21} }$

Step-by-step explanation:

$\cos\theta =\frac{-2}{5}$

As both $sin\,\theta$ ,

$\theta$ lies in the third quadrant.

In the third quadrant,

$\sin\theta$

$\sin\,\theta =-\sqrt{1-\cos^2\,\theta} \\=-\sqrt{1-(\frac{-2}{5})^2 } \\\\=-\sqrt{1-\frac{4}{25} }\\\\=-\sqrt{\frac{25-4}{25} }\\\\=-\frac{\sqrt{21} }{5}$

$\tan\,\theta = \frac{\sin\,\theta}{\cos\,\theta }\\\\=\frac{\frac{-\sqrt{21} }{5} }{\frac{-2}{5} }\\\\=\frac{\sqrt{21} }{2}$

$\sec\,\theta =\frac{1}{\cos\,\theta }\\\\=\frac{1}{\frac{-2}{5} }\\\\=\frac{-5}{2}$

$\ cosec \,\theta = \frac{1}{sin\,\theta }\\\\=\frac{1}{\frac{-\sqrt{21} }{5} }\\\\=\frac{-5}{\sqrt{21} }$

$\cot\,\theta =\frac{1}{\tan\,\theta}\\\\=\frac{1}{\frac{\sqrt{21} }{2} }\\\\=\frac{2}{\sqrt{21} }$

3 0

3 years ago

HELP !!!! can someone help me please how can i use the vertex formula to find this equation for this graph ?

DedPeter [7]

Based on that table of values, we know the highest point(vertex) is at 0.9, 5.9

we can also use just one another point... say 1.4, 4.6

$\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
y=a(x-{{ h}})^2+{{ k}}
\end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\$

$\bf \begin{cases}
h=0.9\\
k=5.9
\end{cases}\implies y=a(x-0.9)^2+5.9
\\\\\\
\begin{cases}
\textit{another point}\\
x=1.4\\
y=4.6
\end{cases}\implies 4.6=a(1.4-0.9)^2+5.9
\\\\\\
4.6=a(0.5)^2+5.9\implies 4.6-5.9=a(0.5)^2\implies -1.3=a(0.5)^2
\\\\\\
\cfrac{-1.3}{0.5^2}=a\implies -5.2=a
\\\\\\
thus\qquad \qquad \boxed{y=-5.2(x-0.9)^2+5.9}$

5 0

3 years ago

Write in the slope-intercept form an equation of the line that passes through the given points.

cluponka [151]

Answer:

y=17/3x-26

Step-by-step explanation:

So what you need to do is find the slope and y-intercept. Then, you write it in y=mx+b form. m=slope, b=y-intercept. So in this case, 17/3 is the slope, and -26 is the y-intercept. Hope this helps :)

7 0

3 years ago

What is the solution to the equation? √2x+10 -6=2

klio [65]

$\sqrt{2x+10} -6=2
$
$\sqrt{2x+10} =8$ we switched side of -6 and added it to 2
2x + 10 = 64 now we squared both sides to get rid of square root
2x = 54 we switched side of +10 and subtracted it from 64
x = 27 we divided both sides with 2

answer is x = 27

7 0

3 years ago

Read 2 more answers

A) 31° B) 42° C) 53° D) 149°

Korolek [52]

Answer:

C. 53°

Step-by-step explanation:

< l = 149° - 96°

<l = 53°

Hope it will help :)❤

3 0

3 years ago

Read 2 more answers