What Quadrants Is Sine Negative?

Which quadrant is sin positive and tan negative?

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.

In the third quadrant, the values for tan are positive only..

Is Quadrant 4 positive or negative?

For an angle in the fourth quadrant the point P has positive x coordinate and negative y coordinate. Therefore: In Quadrant IV, cos(θ) > 0, sin(θ) < 0 and tan(θ) < 0 (Cosine positive). The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.

Can a sine be greater than 1?

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. … Because a ≤ c, sin ∠A ≤ 1 (the only way sin∠A = 1 is if a = c, but that would make for a strange triangle!), the sine ratio cannot be greater than 1.

What are the four quadrants?

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

What quadrant is sin less than 0?

Quadrant IVThe only quadrant where x is positive, so cos(x)>0 , and y is negative, so sin(x)<0 , is quadrant iv .

Is sin 1 the same as 1 sin?

The notation sin-1(x) has been misunderstood to mean 1/sin(x). … So sin-1(x) means the inverse sine of x, that is, the function that undoes the sine function. It is not equal to 1/sin(x).

What is Arcsin equal to?

The arcsin function is the inverse of the sine function. It returns the angle whose sine is a given number….arcsin.sin30 = 0.5Means: The sine of 30 degrees is 0.5arcsin 0.5 = 30Means: The angle whose sin is 0.5 is 30 degrees.

Can a triangle have a negative side?

The sum of the two sides should always be greater than the length of one side in order for the figure to be a triangle. … Moreover, side lengths of triangles cannot be negative, so we can disregard this inequality.

Can a sine be negative?

As a result, sine will be positive, but cosine will be negative, and all tangent values will be negative.) In the third quadrant, all x and y values will be negative, so all sine and cosine values will be negative.

Why cosine of negative angle is positive?

Now the measure of the angle is -m, a negative value when measured clockwise is, because all angles have to be acute to apply the various trigonometrical ratios or relations. Hence, cosine of a negative angle changes into a positive value.

In which quadrant is θ located if Cosθ is positive and Cotθ is negative?

Answer Expert Verified. cos θ is positive in 1st and 4th quadrants. For cot θ be negative, sin θ should be negative, because cos θ is positive.

What does negative sine mean?

The negative -θ of an angle θ is the angle with the same magnitude but measured in the opposite direction from the positive x-axis. … When a point (a,b) is reflected in the x-axis, it moves to the point (a,-b). So Q also has coordinates (cos(θ),-sin(θ)).

Is Sin positive or negative in Quadrant 1?

1 Answer. Ken C. All the trig functions are positive in Quadrant 1. 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 quadrants is sin restricted to?

The arcsine of a positive number is a first quadrant angle, sin-1(+) is in quadrant I. The arcsine of zero is zero, sin-1(0) is 0. The arcsine of a negative number is a negative first quadrant angle, sin-1(-) is in quadrant -I, a clockwise-angle of less than or equal to – /2.

Is sin 1 the same as CSC?

Sine of an angle is the side of the triangle that does not touch the angle divided by the hypotenuse. … cosecant is the reciprical of the sin function or 1/sin(x) so that csc(x)*sin(x) = 1 when it is defined. The two can be confused since arcsin(x) is often denoted as sin^-1(x) and x^-1 is 1/x.