Quick Answer: Can Trig Ratios Be Negative?

Can you have a negative sine?

In the third quadrant, all x and y values will be negative, so all sine and cosine values will be negative.

The final quadrant is the fourth quadrant, and there, all x values are positive, but all y values are negative, so sine will be negative, cosine will be positive and tangent values will be negative..

What is negative cosine equal to?

cos(-θ) = cos θ & sin(-θ) = – sin θ. These are the negative angle identities. Although the diagram shows the angle θ in the first quadrant, the same conclusion can be reached when θ lies in any quadrant, and so the negative angle identities hold for all angles θ.

What is CSC of an angle?

In a right angled triangle, the cosecant of an angle is: The length of the hypotenuse divided by the length of the side opposite the angle. The abbreviation is csc. csc θ = hypotenuse / opposite.

Is Tan positive quadrant 4?

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.

How do you know if a trigonometric ratio is positive or 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. Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values.

How do you prove sin 45?

In a right triangle, one angle is, by definition, 90 degrees so the two acute angles sum to 180- 90= 90 degrees. To prove that sin(45 (degrees)) is 1√2 , consider that if a right triangle has one angle with measure 45 degrees then the other acute angle is 90- 45= 45 degrees also.

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 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.

Is Quadrant 1 positive or negative?

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.

What happens when sine is 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.

Which is the COS 30?

Cos 30° = √3/2 is an irrational number and equals to 0.8660254037 (decimal form). Therefore, the exact value of cos 30 degrees is written as 0.8660 approx. √3/2 is the value of Cos 30° which is a trigonometric ratio or trigonometric function of a particular angle.

What does sin to the negative 1 mean?

Quick Answer: For a right-angled triangle: The sine function sin takes angle θ and gives the ratio opposite hypotenuse. The inverse sine function sin-1 takes the ratio oppositehypotenuse and gives angle θ And cosine and tangent follow a similar idea.

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.

What is the ASTC rule?

The abbreviation for ‘all sin cos tan’ rule in trigonometry is ASTC . The first letter of the third word T indicates that tangent and its reciprocal is positive in the third quadrant. … The first letter of the last word C indicates that cosine and its reciprocal are positive in the fourth quadrant.

What are the four quadrants?

The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown.

How do you find negative trig functions?

Based on the unit circle, the negative angle identities (also called “odd/even” identities) tell you how to find the trig functions at -x in terms of the trig functions at x. In other words, they relate trig values at opposite angles x and -x. For example, sin(-x) = -sin(x), cos(-x) = cos(x), and tan(-x) = -tan(x).

Which quadrants is cosine negative?

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).

What does negative angle mean?

: an angle generated in a direction opposite to an arbitrarily chosen usually clockwise direction.

What is a negative angle in trigonometry?

Definition. Negative Angle. A negative angle is an angle measured by rotating clockwise (instead of counterclockwise) from the positive x axis.