Angles greater than 90° The only difference is that now x or y (or both) can be negative because our angle can now be in any quadrant. It follows that the trigonometric ratios can turn out to be negative or positive.

Can a sine function be negative?

The intersections of this graph and the x-axis are still at x=0, x=pi, and x=2pi. The difference with a negative value of a however, is our sine curve now has a negative amplitude. In other words, our graphs are the same as when a was a positive value, but are now reflected across the x-axis.

Which trigonometric functions are positive and negative?

What this tells us is that if we have a triangle in quadrant one, sine, cosine and tangent will all be positive. In quadrant two, only sine will be positive while cosine and tangent will be negative.

Where are trig functions positive and 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.

Can the amplitude of a trig function be negative?

An amplitude cannot be negative since it is defined as a half the distance, which cannot be negative, between the maximum value and the minimum value. I hope that this was helpful.

Trigonometry - Negative angle identities

16 related questions found

Is amplitude always positive?

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).

Can a cosine be negative?

However, as we are in the third quadrant, cosine must be negative! Therefore, our true cosine is. .

Is wave always positive?

No, the amplitudes of waves are always positive. The amplitude or the peak amplitude of a given wave or vibration offers a way to measure the deviation from its central value.

Can a vertical shift be negative?

A vertical shift is the result of adding a constant term to the value of a function. A positive term results in an upward shift, and a negative term in a downward shift.

Can you have negative frequency?

If frequency is defined as an absolute number then there can be no negative frequencies, but if it is a real number negative frequencies can exist. ... You do need two signals to distinguish between positive and negative frequencies, the same as you need two numbers to define a complex number.

Can a midline be negative?

The sine function y = sin(x) varies up and down around a midline at y = 0 with an amplitude of 1 . The data has a larger amplitude, and it varies around a midline above y = 0 (the outputs are never negative). We can approximate the data's midline by taking an average value of the outputs.

What is negative sine?

The negative angle identities give the relationship between trigonometric functions when we take the trigonometric function of a negative angle. These negative angle identities are as follows. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)

What happens when a is negative?

In conclusion, as the magnitude of a increases, the graph of the parabola becomes narrower, and as the magnitude of a decreases, the graph of the parabola becomes wider. If a is negative, the graph of the parabola opens down instead of up.

Can amplitude of cosine graph be negative?

Fraction values between 0 and 1 make the graph shorter.

Before you multiply a sine or cosine function by 2, for instance, its graph oscillated between –1 and 1; now it moves between –2 and 2. its amplitude is still 5. The negative sign just flips the graph upside down.

How does amplitude affect a sine graph?

When 0 < a < 1, the amplitude of the graph decreases, causing the slopes of the graph to appear more "flat". When a > 1, the amplitude of the graph increases, causing the slopes of the graph to appear more "steep". This shows that changing the a affects the amplitude of the graph.

What trig functions are negative in the second quadrant?

In the second quadrant, the x-values are negative, so x/r and y/x are negative; only y/r is positive, so only the Sine is positive in QII. In the third quadrant, each of x and y is negative, so x/r and y/r are negative; only y/x is positive, so only the Tangent is positive in QIII.

What quadrant is cosine positive and sine negative?

Trigonometric functions sine and cosine are both positive in first quadrant but in third quadrant both are negative. Hence in these two quadrants they have same sign. However, in second quadrant while sine is positive, cosine is negative. And in fourth quadrant, cosine is positive and sine is negative.

What is negative amplitude of a wave?

If the electric field 'wave' has a 'negative' amplitude, it just signifies that the electric field vector at that particular point is in the opposite direction of positive.

What is positive and negative amplitude?

The Positive peak amplitude can be defined as “the magnitude of a crest in the positive side of a cycle”. The Negative peak amplitude can be defined as “the magnitude of a trough in the negative side of a cycle”.