Question: Can Hypotenuse 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..

Is hypotenuse always positive in unit circle?

As the hypotenuse is (x^2+y^2)^1/2 which will always have a positive value so hypotenuse is always positive.

Can the side of a triangle be negative?

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.

Is the hypotenuse always the longest side?

The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem.

Where is SEC negative?

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 are the 4 quadrants of time management?

The Four Quadrants of Time ManagementImportant and Urgent – Crises and Emergencies.Important but Not Urgent – Prevention, Planning, and Improvement.Not Important but Urgent – Interruptions and Busy Work.Not Important and Not Urgent – Time Wasters.

Why is my cosine 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 cosine decreases in magnitude but is now negative, so, the cosine increases from its minimum of -1 to a value of 0.

Can cosine 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. Tangent will be positive because a negative divided by a negative is positive.)

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.

What is SEC equal to?

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 .

What 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.

What are the 4 quadrants?

These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise. Locations on the coordinate plane are described as ordered pairs.

Is Quadrant 1 positive or negative?

Four QuadrantsQuadrantX (horizontal)Y (vertical)IPositivePositiveIINegativePositiveIIINegativeNegativeIVPositiveNegative

What are the 3 sides of a triangle called?

Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs.

Does 4 5 6 make right triangles?

Explanation: For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Hence 4 , 5 and 6 are not pythagorean triple.

Does 20 25 15 represent a right triangle?

The largest length is always the hypotenuse. If we were to multiply any triple by a constant, this new triple would still represent sides of a right triangle. Therefore, 6, 8, 10 and 15, 20, 25, among countless others, would represent sides of a right triangle.

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.