If cos theta = 0.3090, which of the following represents approximate values of sin thetha for 0 degrees <90 degrees? A. sin thetha =0.9511;tan theta = 0.3249 B.sin thetha =0.…

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asked Jun 7, 2019 44.1k views

2 Answers

Nikita Goncharov · Answer 1 · 2019-06-09T02:34:01+0000

Answer:

The correct option is B)
$\sin\theta\approx0.9511$ ;
$\tan\theta\approx3.078$ .

Explanation:

Consider the provided value of trigonometry function.

$\cos \theta = 0.3090$

Use the identity:
$\sin^2\theta+\cos^2\theta=1$

$\sin^2\theta=1-\cos^2\theta$

$\sin\theta=√(1-\cos^2\theta)$

Now substitute
$\cos \theta = 0.3090$

$\sin\theta=√(1-(0.3090)^2)$

$\sin\theta\approx0.9511$

Hence, the value of
$\sin\theta\approx0.9511$ .

Now, use the identity
$\tan\theta=(\sin\theta)/(cos\theta)$

Substitute the respective values.

$\tan\theta=(0.9511)/(0.3090)$

$\tan\theta\approx3.078$

Hence, the value of
$\tan\theta\approx3.078$ .

Blexy · Answer 2 · 2019-06-11T01:21:04+0000

In this question, the given value is

$cos \theta = 0.3090$

And we have to find the value of sin theta and tan theta where theta is in first quadrant .

And in first quadrant, all are positive .

Now we use the formula, which is

$sin \theta = √(1-cos^2 \theta) = √(1 - 0.3090^2) = 0.9511$

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

$tan \theta = (sin \theta)/( cos \theta) = (0.9511)/(0.3090) =3.078$

So the correct option is B .