If sin theta = -5/7 , which of the following are possible? A) cos theta = √24/7 , and tan theta = 5/√24 B) cos theta = -√24/7, and tan theta = 5/√24 C) sec theta = 7/√24 , and t…

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asked Nov 11, 2019 212k views

2 Answers

Mpaf · Answer 1 · 2019-11-12T00:03:21+0000

It is given that

$sin \theta = (-5)/(7)$

And according to pythagorean identity, we will get

$cos \theta = \pm √(1-sin^2 \theta)$

Substituting the value of sin theta, we will get

$cos \theta = \pm \sqrt{1- (25)/(49)} \\ cos \theta = \pm (√(24))/(7)$

and sec theta is the reciprocal of cos theta.

SO possible values of sec theta are

$sec \theta = \pm (7)/( √(24))$

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

So possible values of tan theta are

$tan  \theta = \pm (5)/( √(24))$

So the correct options are B and C .

LambergaR · Answer 2 · 2019-11-17T13:53:25+0000

Solution:

we are given that

$sin \theta=-5/7$

As we know that

$cos \theta =√(1-sin^2 \theta)  \\$

Substitute the value we get

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

Since
$sec \theta=(1)/(cos \theta)\\$

So here
$sec \theta=(7)/(√(24))\\$

As we know that

$tan \theta=(sin \theta)/(cos \theta)\\ \\  \text{Substitute the values we get}\\ \\ tan \theta=(-5/7)/((√(24))/(7))\\ \\ tan \theta=(-5)/(√(24))\\$

Hence the correct option is C.