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A Smart Trig Class:… is one example of a mnemonic device that can be used to recall the signs of the trig functions sine, cosine, and tangent (sine/cosine) in each of the four quadrants. In the first and second quadrants, each of the three trig functions returns a positive value. In Quadrant II, the only positive value is Sine; all of the other values are negative.
In which quadrants does the sine have a positive value?
Quadrant 2 has positive values for sine and cosecant, whereas Quadrant 3 has positive values for tangent and cotangent, and Quadrant 4 has positive values for secant and cosine.
Why does the sin evaluate to a positive number in quadrants I and II?
As sine is the second coordinate on point P, it is going to be positive anytime that point is above the x axis. This is because sine is the cosine of the angle between the point and the x axis. It refers to the first and second quadrants. These are the two quadrants that are located above the x-axis of the diagram.
In the second quadrant, does sine have a positive or negative sign?
The sine (and cosec) functions produce favorable results in the second quadrant (II). The values of tan and cotan are both positive in the third quadrant (III). Positive values for cos and sec can be found in the fourth quadrant (IV).
In which quadrants does the negative sine appear?
Explanation: In the first quadrant, the sine and cosine functions of trigonometry both have positive values; however, in the third quadrant, both values have negative values.
Providing an explanation as to why the sine, cosine, and tangent of an angle are either positive or negative in different quadrants.
25 questions found to be related.
How are you able to determine which quadrant represents positive or negative values?
In Quadrant I, the x-coordinate and the y-coordinate are both positive. In Quadrant II, the x-coordinate is negative, but the y-coordinate is positive. In Quadrant III, both the x- and the y-coordinates are negative. In Quadrant IV, the x-coordinate is positive, but the y-coordinate is negative.
What is it that makes the second quadrant a positive one?
Angles as Signals in the Four Quadrants
Only the sine and the cosecant (which is the reciprocal of sine) have a positive value in the second quadrant. Tangent and cotangent are the only two functions that return a positive value in the third quadrant. Eventually, in the fourth quadrant, the only components that have a positive value are the cosine and the secant.
In quadrant II, does the function cot t evaluate to a positive or a negative value?
Only sine and its reciprocal function, cosecant, have a positive value in quadrant II, sometimes known as the “Smart” quadrant. In quadrant III, sometimes known as “Trig,” the only functions that have a positive value are tangent and its reciprocal function, cotangent.
In Quadrant IV, does the function tan T evaluate to a positive or a negative value?
Although sine and cosine both have a negative sign, the tangent of an angle whose terminal arm is in Quadrant III is positive since tangent is the sum of sine and cosine. As sine is a negative number and cosine is a positive number, the tangent of an angle whose terminal arm is in Quadrant IV is also a negative number.
Where can I find the positive of sin, cos, and tan?
The “cast” Rule in Addition to Quadrants
All of the values for sin, cos, and tan are positive when looking at the first quadrant. Only positive values for sin can be found in the second quadrant of the chart. Only positive values for tan can be found in the third quadrant of the chart. Only positive values for cos may be found in the fourth quadrant of the graph.
In which quadrant does an angle’s sine have a positive value while its cosine has a negative value?
If a point lies in the third quadrant, the acute angle with a measure less than 180 degrees is referred to as the related angle for. In conclusion, if the angle is between 270 and 360 degrees, the point P that corresponds to it is in the fourth quadrant. Within this particular quadrant, we can observe that the ratios of sine and tangent are both negative, however the ratio of cosine is positive.
What quadrant is 282 degrees in?
The angle can be found in the fourth quadrant of the diagram.
Where exactly does the point 2 3 fall within the chart?
The point (2,−3) sits in the third quadrant.
Where exactly is the fourth quadrant located?
The bottom right hand corner of the plane marks the beginning of the fourth quarter of the plane. In this coordinate X has positive values while y has negative values.
What is the quadrant of 1 2?
Algebra Examples
Because x has a negative value and y has a positive value, the point lies in the second quadrant of the graph.
Why are the COS and SEC values always going to be positive?
If, in accordance with trigonometric ratios, sin (-A) = sinA, the following question begs to be answered: why does cos (-A)=cosA? … C stands for cos, while the reciprocal of sec, which is positive in the fourth quadrant, is denoted by the symbol sec. Because A is located in the fourth quadrant, sin(-A) is equal to sin(-A).
What part of the quadrant does angle fall under?
Quadrants & Quadrantal Angles
The first quadrant has the angles that range from 0 degrees to 90 degrees. The second quadrant is comprised of angles that range from 90 degrees to 180 degrees. The third quadrant has the angles that range from 180 degrees to 270 degrees. The fourth quadrant contains the angles that range from 270 degrees to 360 degrees.
In which quadrants does the positive value of a point’s abscissa appear?
A coordinate is an ordered pair of numbers, with the first number being the abscissa, or the measurement along the X axis. A coordinate can be used to describe the location of an object. Thus, the point’s abscissa is positive in the first and fourth quadrants where it is located.