Question

if theta is in the first quadrant sin left parenthesis t h e t a right parenthesis equals 0.17 then what is tan left parenthesis theta right parenthesis rounded to the nearest thousandth?

Answer 1

The value of $tan\theta$ in the first quadrant is approximately 0.173.

There are 4 quadrants inside the cartesian aircraft. All trigonometric ratios of sin, cos, tan are high quality inside the first quadrant.in the 2nd quadrant simplest sin is advantageous rest are negative.  within the 1/3 quadrant simplest tan is wonderful inside the fourth quadrant best cos is fantastic.

Given $sin \theta=0.17$ and $\theta$ is in the first quadrant.

We know from trigonometrical identities that

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

Substituting the value of  $sin \theta$ in the above equation we get:

$or, (0.17)^2+cos^2\theta=1\\or,cos^2\theta=1-0.0289\\or.cos\theta=\pm\sqrt{0.9711}\\or,cos\theta=\pm 0.98544...$

As $\theta$ lies in the first quadrant then the value of $cos\theta$ is positive.

∴$cos\theta\approx0.98544$

From the properties of trigonometry we know that :

$tan\theta=\frac{sin\theta}{cos\theta}$

$or,tan\theta=\frac{0.17}{0.98544} \\or,tan\theta=0.17251\\or,tan\theta\approx0.173$

The value of $tan\theta$ is approximately 0.173 to the nearest thousandth . The value is positive as the angle lies in the first quadrant.

To learn more about quadrant and trigonometric ratios:

brainly.com/question/7196312

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