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Sagot :
The value of tangent theta is equal to the negative 1. At this value the value of secant theta is [tex]\sqrt{2}[/tex].
What is tangent theta?
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]\rm tan\theta=\dfrac{sin \theta}{cos \theta}[/tex]
Given information-
The value of tangent theta is equal to the negative 1.
[tex]\tan \theta=-1[/tex]
The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,
[tex]\rm tan\theta=\dfrac{sin \theta}{cos \theta}[/tex]
The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,
[tex]\rm -1=\dfrac{sin \theta}{cos \theta}\\[/tex]
Simplify it further as,
[tex]\rm -cos \theta=sin \theta[/tex]
When the value of cosine and sine theta is equal, then the angle exist in 4th quadrant with the value of [tex]\dfrac{7\pi}{4}[/tex]. Which extent to the [tex]\sqrt{2}/2[/tex] for the cosine function.
In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,
[tex]\rm \dfrac{1}{sec\theta}=\dfrac{\sqrt{2}}{2}\\sec\theta=\sqrt{2}[/tex]
Thus the value of secant theta is [tex]\sqrt{2}[/tex]
Learn more about the tangent theta here;
https://brainly.com/question/29190
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