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In quadrant I, which is “A,” all of the six trigonometric functions are positive. In quadrant II, “Smart,” only sine and its reciprocal function, cosecant, are positive. In quadrant III, “Trig,” only tangent and its reciprocal function, cotangent
, are positive.
Which quadrant is sine and cosecant positive?
Signs of Angles in Quadrants
Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values. In the second quadrant, only sine and cosecant (the reciprocal of sine) are positive. In the third quadrant, only tangent and cotangent are positive.
Which is positive in which quadrant?
In Quadrant I, both the x- and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV, x is positive but y is negative.
Which sides are cosecant?
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
In what quadrants is Secant negative?
Since r is a radius, it must be positive, so sec(x) is negative anywhere x is negative. This is in Quadrants II and III .
Trigonometry – The signs of trigonometric functions
19 related questions found
Is SEC negative in the third quadrant?
In the third quadrant (III), tan (and cotan) are positive. In the fourth quadrant (IV), cos (and sec) are positive.
What quadrants can secant be in?
Sine and cosecant are positive in Quadrant 2, tangent and cotangent are positive in Quadrant 3, and cosine and secant are positive in Quadrant 4.
What two sides are needed for the cosecant function?
The cosecant function, abbreviated csc, is the reciprocal of the sine function and thus uses this ratio: hypotenuse/opposite. The hypotenuse of a right triangle is always the longest side, so the numerator of this fraction is always larger than the denominator.
How do you find cosecant?
The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .
Is quadrant 4 positive or negative?
Quadrant III: Both x and y-coordinate are negative. Quadrant IV: x-coordinate is positive and y-coordinate is negative.
Which quadrants are positive and negative on a graph?
The first quadrant is the upper right-hand corner of the graph, the section where both x and y are positive. The second quadrant, in the upper left-hand corner, includes negative values of x and positive values of y. The third quadrant, the lower left-hand corner, includes negative values of both x and y.
In which quadrant does the point (- 1 2 lie?
(-1,-2)lies in Third Quadrant.
What quadrant is sine positive?
Quadrants and the “cast” Rule
In the first quadrant, the values for sin, cos and tan are positive. In the second quadrant, the values for sin are positive only.
Why is sin positive in second quadrant?
Since sine is the second coordinate on point P, it’s going to be positive whenever that point is above the x axis. That means quadrants 1 and 2. Those are the 2 quadrants that are above the x axis. … Cosine is positive to the right of the y axis.
What is cosecant made of?
The cosecant of an angle in a right triangle is a relationship found by dividing the length of the hypotenuse by the length of the side opposite to the given angle. This is the reciprocal of the sine function.
What is the opposite of CSC?
Cosecant Function: csc(θ) = Hypotenuse / Opposite. Secant Function: sec(θ) = Hypotenuse / Adjacent.
What does CSC graph look like?
The vertical asymptotes of cosecant drawn on the graph of sine. … The cosecant goes down to the top of the sine curve and up to the bottom of the sine curve. After using the asymptotes and reciprocal as guides to sketch the cosecant curve, you can erase those extra lines, leaving just y = csc x.
Is the function SEC T positive or negative in quadrant II?
Answer: The function sec t is negative in quadrant ii.
What quadrant is an angle in?
Quadrants & Quadrantal Angles
Angles between 0∘ and 90∘ are in the first quadrant. Angles between 90∘ and 180∘ are in the second quadrant. Angles between 180∘ and 270∘ are in the third quadrant. Angles between 270∘ and 360∘ are in the fourth quadrant.