Where Is Cos Negative?

Where does sin equal?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram)..

Which quadrants is tan negative?

The tangent ratio is y/x, so the tangent will be negative when x and y have opposite signs. This occurs in the second quadrant (where x is negative but y is positive) and in the fourth quadrant (where x is positive but y is negative).

How can sin be negative?

Both x and y coordinates are negative in the third quadrant. Since the hypotenuse is a +1, both the sine and the cosine must be negative. As the angle increases from 180° to 270°, the sine increases in magnitude but is now negative, so, the sine decreases from 0 to -1.

What is F to the negative 1 power?

Notation. The inverse of the function f is denoted by f -1 (if your browser doesn’t support superscripts, that is looks like f with an exponent of -1) and is pronounced “f inverse”. Although the inverse of a function looks like you’re raising the function to the -1 power, it isn’t.

What does sin to the negative 1 mean?

The inverse sin of 1, ie sin-1 (1) is a very special value for the inverse sine function. Remember that sin-1(x) will give you the angle whose sine is x . Therefore, sin-1 (1) = the angle whose sine is 1.

Can Cotangent be negative?

Signs of Angles in Quadrants The distance from a point to the origin is always positive, but the signs of the x and y coordinates may be positive or negative. … In the second quadrant, only sine and cosecant (the reciprocal of sine) are positive. In the third quadrant, only tangent and cotangent are positive.

Is Tan Sin over COS?

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x . … 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 the unit circle Sin Cos?

The point of the unit circle is that it makes other parts of the mathematics easier and neater. For instance, in the unit circle, for any angle θ, the trig values for sine and cosine are clearly nothing more than sin(θ) = y and cos(θ) = x. This can be helpful for remembering the trig values.) …

What is the range of Cos?

Also, the value of cos(x), depending on the point on the circle, can go to a maximum of 1 at x = 0 degrees and a minimum of -1 at x = 180 degrees. So, the range of cos(x) is from -1 to 1.

Where is Cos positive?

In the fourth quadrant, Cos is positive, in the first, All are positive, in the second, Sin is positive and in the third quadrant, Tan is positive. This is easy to remember, since it spells “cast”. These angles are “related angles” and their cosines and tangents will be related in a similar way.

Where is CSC negative?

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 Quadrant is sec negative?

Quadrant IIIIn Quadrant III, cot ⁡ θ \displaystyle \cot{\theta} cotθ is positive, csc ⁡ θ \displaystyle \csc{\theta} cscθ and sec ⁡ θ \displaystyle \sec{\theta} secθ are negative.

Where is Secx undefined?

THE SECANT FUNCTION The secant, sec x, is the reciprocal of the cosine, the ratio of r to x. When the cosine is 0, the secant is undefined. When the cosine reaches a relative maximum, the secant is at a relative minimum.

Where is cos not defined?

Sine and cosine functions are never undefined on unit circle. They are defined at every point of a unit circle. Because according to definitions of Sine and cosine, cosine is the x-coordinate of a point moving along unit circle. Likewise, Sine is the y-coordinate of that moving point.

Where is Cos negative on the unit circle?

Therefore: In Quadrant II, cos(θ) < 0, sin(θ) > 0 and tan(θ) < 0 (Sine positive). For an angle in the third quadrant the point P has negative x and y coordinates. Therefore: In Quadrant III, cos(θ) < 0, sin(θ) < 0 and tan(θ) > 0 (Tangent positive).

Why is tan 90 undefined?

tan90∘ is undefined because you can’t divide 1 by nothing. Nothing multiplied by 0 will give an answer of 1 , so the answer is undefined.