Is Cosine Ever Negative?

Can hypotenuse be negative?

Because it is the length of the distance from one end of the hypotenuse to the other.

Length from one point to the other point can never be negative.

So by this logic, hypotenuse of triangle (and for that matter, any length) can not be negative and so should be positive..

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 is sin (- theta?

The right triangle formulas are the most important ones in the trigonometry. The sin Theta is the ratio of the opposite side to the hypotenuse, If theta (Θ)

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.

Why is negative cosine 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.

Is the hypotenuse always the longest side?

The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle. Comment on Charlotte Auen’s post “The shortest side is the one opposite the smallest…”

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’s the difference between a sin and cos graph?

In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.

How do you find sin?

Sin, Cos and TanThe sine of the angle = the length of the opposite side. the length of the hypotenuse.The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.The tangent of the angle = the length of the opposite side. the length of the adjacent side.

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.

What Quadrant is sec negative?

Signs of Angles in Quadrants In the second quadrant, only sine and cosecant (the reciprocal of sine) are positive. In the third quadrant, only tangent and cotangent are positive. Finally, in the fourth quadrant, only cosine and secant are positive.

Is Cos 90 minus theta?

All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out Sin Theta = Cos (90 – Theta) and Cos Theta = Sin (90 – Theta).

Can an amplitude be negative?

The amplitude or peak amplitude of a wave or vibration is a measure of deviation from its central value. Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120).

What does a negative cosine graph look like?

Hare – sign is in front of the cosine graph. If we draw the negative cosine it will produce the reflection about the x – axis. So the negative cosine graph will be opposite to the positive graph.

Is Cos negative quadrant 2?

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

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.

How often does cosine repeat?

As the point P moves round the unit circle in either the clockwise or anticlockwise direction, the cosine curve above repeats itself for every interval of 360˚. Its period is 360˚.