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MakcuM [25]
3 years ago
13

If sin theta = -5/7 , which of the following are possible?

Mathematics
2 answers:
Sav [38]3 years ago
5 0

Solution:

we are given that

sin \theta=-5/7

As we know that

cos \theta =\sqrt{1-sin^2 \theta}  \\

Substitute the value we get

cos \theta=\sqrt{1-(\frac{-5}{7})^2}  \\
\\
cos \theta=\sqrt{1-(\frac{25}{49})}  \\
\\
cos \theta=\sqrt{(\frac{24}{49})} =\frac{\sqrt{24}}{7}\\

Since sec \theta=\frac{1}{cos \theta}\\

So here sec \theta=\frac{7}{\sqrt{24}}\\

As we know that

tan \theta=\frac{sin \theta}{cos \theta}\\
\\  \text{Substitute the values we get}\\
\\
tan \theta=\frac{-5/7}{\frac{\sqrt{24}}{7}}\\
\\
tan \theta=\frac{-5}{\sqrt{24}}\\

Hence the correct option is C.

aleksklad [387]3 years ago
5 0

It is given that

sin \theta = \frac{-5}{7}

And according to pythagorean identity, we will get

cos \theta = \pm \sqrt{1-sin^2 \theta}

Substituting the value of sin theta, we will get

cos \theta = \pm \sqrt{1- \frac{25}{49}}
\\
cos \theta = \pm \frac{\sqrt{24}}{7}

and sec theta is the reciprocal of cos theta.

SO possible values of sec theta are

sec \theta = \pm \frac{7}{ \sqrt{24}}

And tan theta is the ratio of sin theta and cos theta

So possible values of tan theta are

tan  \theta = \pm \frac{5}{ \sqrt{24}}

So the correct options are B and C .

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