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vazorg [7]
3 years ago
6

Hi

Mathematics
1 answer:
Alona [7]3 years ago
5 0
You’re absolutely amazing and I really appreciate that you’re trying to help others! And if you need anything yourself please feel free to ask :)
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Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than th
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The value of tangent theta is equal to the negative 1.  At this value the value of secant theta is \sqrt{2}.

<h3>What is tangent theta?</h3>

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

\rm tan\theta=\dfrac{sin \theta}{cos \theta}

Given information-

The value of tangent theta is equal to the negative 1.

\tan \theta=-1

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

\rm tan\theta=\dfrac{sin \theta}{cos \theta}

The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,

\rm -1=\dfrac{sin \theta}{cos \theta}\\

Simplify it further as,

\rm -cos \theta=sin \theta

When the value of cosine and sine theta is equal, then the angle exist in 4th quadrant with the value of \dfrac{7\pi}{4}. Which extent to the \sqrt{2}/2 for the cosine function.

In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,

\rm \dfrac{1}{sec\theta}=\dfrac{\sqrt{2}}{2}\\sec\theta=\sqrt{2}

Thus the value of secant theta is \sqrt{2}

Learn more about the tangent theta here;

brainly.com/question/29190

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