Question

The terminal side of an angle in standard position passes through p(–3, –4). What is the value of ?

Answer 1

Answer:

233.1°

Step-by-step explanation:

As we know that

An angle has two rays. One is called intial ray from where it starts and other is called terminal ray where it ends.

We are given that

Angle is ending at the point = (-3, -4)

Since the sign of both x and y are negative, it means terminal arm of the angle is in the 3rd quadrant.

As we know that

$tan\theta =\frac{y}{x}$

$tan\theta =\frac{-4}{-3}$

$\theta =tan^{-1}(\frac{-4}{-3})$

$\theta =tan^{-1}(\frac{-4}{-3})$

$\theta =53.1\textdegree$

Now, as the angle lies in 3rd quadrant, therefore we need to add 180 into 53.1° to get our desired angle.

$\alpha =180 +\theta =180\textdegree + 53.1\textdegree = 233.1\textdegree$

   

Answer 2

Concept:

The position of an angle with its vertex at the origin of a rectangular-coordinate system and its initial side coinciding with the positive $x-$axis.

Given:

We are only if the terminal side of an angle in standard position passes through $p(-3,-4)$.

Find:

We have find the worth of $\tan \theta$.

Solution:

When two rays start from a typical point, an angle is created. The common point is termed the vertex.

An angle is in standard position if the vertex lies at origin and also the initial arms lie along the positive $x-$axis.

As the terminal side passes through $p(-3, -4)$

The terminal arm lies in $IV$ Quadrant.

The ratio of the alternative side to the adjacent side is named the tangent.

From triangle, we all know that,

$\tan \theta = \frac{Opposite}{Adjacent}$

Substituting the values

$\tan \theta = \frac{-4}{-3}\\ \tan \theta=\frac{4}{3}$

So we get,

$\theta = 53.130$

Hence, the worth of$\tan \theta$is $\frac{4}{3}$.

#SPJ3