Question

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 =0.9511 ;tan thetha =3.0780 C. sin thetha 3.2362 ; tan thetha=0.0955
D. sin thetha = 3.2362;tan thetha=10.4731

Answer 1

Answer:

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

Step-by-step explanation:

Consider the provided value of trigonometry function.

$\cos \theta = 0.3090$

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

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

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

Now substitute $\cos \theta = 0.3090$

$\sin\theta=\sqrt{1-(0.3090)^2}$

$\sin\theta\approx0.9511$

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

Now, use the identity $\tan\theta=\frac{\sin\theta}{cos\theta}$

Substitute the respective values.

$\tan\theta=\frac{0.9511}{0.3090}$

$\tan\theta\approx3.078$

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

Answer 2

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

$sin \theta = \sqrt{1-cos^2 \theta} = \sqrt{1 - 0.3090^2} = 0.9511$

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

$tan \theta = \frac{sin \theta}{ cos \theta} = \frac{0.9511}{0.3090} =3.078$

So the correct option is B .