Root of 2x plus 1/3 square

Mathematics

1 answer:

Ludmilka [50]2 years ago

4 0

Answer:

Here's the answer. Have a good day

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Simplify sin Θ/√1-sin^2 Θ

dedylja [7]

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Simplify the trigonometric expression.

Call the expression E:

$\mathsf{E=\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}\qquad\qquad(but~~1-sin^2\,\theta=cos^2\,\theta)}\\\\\\
\mathsf{E=\dfrac{sin\,\theta}{\sqrt{cos^2\,\theta}}}\\\\\\
\mathsf{E=\dfrac{sin\,\theta}{\left|cos\,\theta\right|}}}$

$\mathsf{E}=\left\{\!\begin{array}{rl}\mathsf{\dfrac{sin\,\theta}{cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta>0}\\\\\mathsf{\dfrac{sin\,\theta}{-\,cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta$

So basically E is equivalent to $\pm\,\mathsf{tan\,\theta},$ where the sign depends on which quadrant $\theta$ lies. Shortly,

$\mathsf{\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}}=\left\{\!
\begin{array}{rl}
\mathsf{tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~1^{st}~or~the~4^{th}~quadrant}\\\\
\mathsf{-\,tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~2^{nd}~or~the~3^{rd}~quadrant}
\end{array}$

I hope this helps. =)

Tags: <em>simplify trigonometric trig expression sine cosine tangent sin cos tan absolute value modulus trigonometry</em>

4 0

3 years ago

Read 2 more answers

Pls help need it real bad

Nikolay [14]

Awnser 26 add them all together

7 0

2 years ago

PLEASE HELP! I feel horrible and I'm crying so hard right now. This is due.

Lady bird [3.3K]

Answer:

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