How are the graphs of the sine function and the cosine function similar?

The graphs of sine and cosine have the same shape: a repeating “hill and valley” pattern over an interval on the horizontal axis that has a length of . The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values .

What is the relationship between sine and cosine graphs?

Relationship between Sine and Cosine graphs



The graph of sine has the same shape as the graph of cosine. Indeed, the graph of sine can be obtained by translating the graph of cosine by ( 4 n + 1 ) π 2 \frac{(4n+1)\pi}{2} 2(4n+1)π​ units along the positive x x x-axis ( n n n is an integer).

What is similar and different about the sine and cosine functions?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

Are sine and cosine similar?

You probably noticed that these cofunction identities all use the difference of angles, but the slide of the sine function to the left was a sum. The shifted sine graph and the cosine graph are really equivalent — they become graphs of the same set of points.

What is the main difference between the sine and cosine graph?

The graph of the cosine is the darker curve; note how it’s shifted to the left of the sine curve. The graphs of the sine and cosine functions illustrate a property that exists for several pairings of the different trig functions.

What do the graphs of sine and cosine have in common with the swing you see?

What do the graphs of sine and cosine have in common with the swinging you see? The shifted sine graph and the cosine graph are really equivalent — they become graphs of the same set of points. …

What is the relationship between sine and cosine of complementary angles?

▫ The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle.

What angles are sine and cosine the same?

The sine and cosine of complementary angles are equal. 90o- 30o=60o,so 60o is complementary to 30o.

For which acute angle are the sine of the angle and cosine of the angle equal?

Summary: The triangle that contains an acute angle for which the sine and cosine ratios are equal is the triangle with angles 90°, 45°, and 45°.

For what angle measurement must sine and cosine have the same value?

There are certain special angles where it is possible to give the exact value of sine and cosine. These are the angles that measure 0°, 30°, 45°, 60°, and 90°; these angle measures are frequently seen.

In which quadrant are both sin theta and cos theta negative?

Thus, in quadrant II lies θ, because sinθ is positive and cosθ is negative.

Are cosine and sine complements or supplements?

So the cosine of an angle is equal to the sine of its complement.

What can a sine value tell you about a point on a circle?

Defining Sine and Cosine Functions



The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle. More precisely, the sine of an angle t equals the y-value of the endpoint on the unit circle of an arc of length t. In Figure 2, the sine is equal to y.

What is the period of the sine function and how do you know?

The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.

What happens when the amplitude of the graph of the sine function increases?

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.

How do the angle measures in degrees compare to those in radians?

Degrees measure angles by how far we tilted our heads. Radians measure angles by distance traveled. or angle in radians (theta) is arc length (s) divided by radius (r). A circle has 360 degrees or 2pi radians — going all the way around is 2 * pi * r / r.

What is the relation between radian and degree?

The magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees ≈ 57.295779513082320876 degrees.

Why do physicist usually use radians instead of degrees for measuring angles?

Radians have the following benefits: They are dimensionless, which means that they can be treated just as numbers (although you still do not want to confuse Hertz with radians per second). Radians give a very natural description of an angle (whereas the idea of 360 degrees making a full rotation is very arbitrary).

What is a conversion rate for radians to degrees and degrees to radians?

1° equals 0.017453 radians and 1 rad equals 57.2958°. To convert an angle from radians to degrees, we multiply it by 180°/π. To convert an angle from degrees to radians, we multiply it by π/180°.

Which function is used to convert an angle from degrees into radians?

To convert degrees to radians, we have to multiply the given angle (that is in degrees) by π/180°. For this, we use the formula: Radians = Degrees × π/180°.

What is the conversion factor used to convert angle measures from degrees to radians?

To convert from degrees to radians, multiply the degrees by π180° radians . Example 1: Convert 60° to radian measure.

How do you convert radian measure to degrees?

To convert from radians to degrees, multiply the radians by 180°π radians . Example 1: Convert π4 radians to degrees.

How do you put your graphing calculator into radian mode?

Video quote: So to enter degree mode all we have to do is press the mode. And then scroll down here where it says Radian or degree. And as you can see Radian is selected.

What is meant by one radian?

Definition of radian



: a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 57.3 degrees.