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

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Riia Riia · Answer 1 · 2018-08-28T13:17:40+02:00

In this question, the given value is

[tex] cos \theta = 0.3090 [/tex]

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

[tex] sin \theta = \sqrt{1-cos^2 \theta} = \sqrt{1 - 0.3090^2} = 0.9511 [/tex]

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

[tex] tan \theta = \frac{sin \theta}{ cos \theta} = \frac{0.9511}{0.3090} =3.078 [/tex]

So the correct option is B .

FelisFelis FelisFelis · Answer 2 · 2019-11-27T05:37:18+01:00

Answer:

The correct option is B) [tex]\sin\theta\approx0.9511[/tex]; [tex]\tan\theta\approx3.078[/tex].

Step-by-step explanation:

Consider the provided value of trigonometry function.

[tex]\cos \theta = 0.3090[/tex]

Use the identity: [tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\sin^2\theta=1-\cos^2\theta[/tex]

[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]

Now substitute [tex]\cos \theta = 0.3090[/tex]

[tex]\sin\theta=\sqrt{1-(0.3090)^2}[/tex]

[tex]\sin\theta\approx0.9511[/tex]

Hence, the value of [tex]\sin\theta\approx0.9511[/tex].

Now, use the identity [tex]\tan\theta=\frac{\sin\theta}{cos\theta}[/tex]

Substitute the respective values.

[tex]\tan\theta=\frac{0.9511}{0.3090}[/tex]

[tex]\tan\theta\approx3.078[/tex]

Hence, the value of [tex]\tan\theta\approx3.078[/tex].