If you know that tan(θ)= -0.707 , which quadrant(s) could θ be found in?
I don't know why it goes in which quadrant
Tangent is negative in Quadrant II and Qadrant IV.
the sign of the value indicates the possible quadrant
"All Students Take Calculus" ... signs of trig functions, starting in Quad I
... All positive in 1st Quad
... Sine positive in 2nd Quad
... Tangent positive in 3rd Quad
... Cosine positive in 4th Quad
To determine in which quadrant(s) the angle θ could be found, we need to consider the sign of the tangent function in each quadrant.
In the first quadrant (0° to 90°), all trigonometric functions are positive. Since tan(θ) is negative (-0.707), θ cannot be in the first quadrant.
In the second quadrant (90° to 180°), only the sine function is positive. Since tan(θ) is negative, θ could potentially be in the second quadrant.
In the third quadrant (180° to 270°), only the tangent function is positive. Since tan(θ) is negative, θ cannot be in the third quadrant.
In the fourth quadrant (270° to 360°), all trigonometric functions are negative. Since tan(θ) is negative, θ could potentially be in the fourth quadrant.
Therefore, θ could be found in either the second quadrant or the fourth quadrant.
To determine in which quadrant(s) θ could be found based on the given value of tan(θ) = -0.707, we need to understand the relationship between tangent and quadrants in the coordinate plane.
The tangent function represents the ratio of the opposite side to the adjacent side of a right-angled triangle. It is positive in the first and third quadrants and negative in the second and fourth quadrants.
Given that tan(θ) = -0.707, which is negative, we can conclude that θ lies in either the second or fourth quadrant.
To further determine the specific quadrant, we can use the fact that tangent is positive when the angle lies between -90° and 90° (first and third quadrants) and negative when the angle lies between 90° and 270° (second and fourth quadrants).
Using inverse tangent (also known as arctan or tan^(-1)), we can find the angle(s) that have a tangent of -0.707.
Using a calculator's inverse tangent function, we find that arctan(-0.707) ≈ -35.26° and 144.74°.
Since arctan(-0.707) gives us two possible angles, θ can be found in both the second quadrant (between 90° and 180°) as well as the fourth quadrant (between 270° and 360°).