What is the use of the unit circle?

The Unit Circle. The point of the unit circle is that it makes other parts of the mathematics easier and neater. For instance, in the unit circle, for any angle θ, the trig values for sine and cosine are clearly nothing more than sin(θ) = y and cos(θ) = x.

Considering this, who is the founder of the unit circle?

For a circle of unit radius the length of the chord subtended by the angle x was 2sin (x/2). The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC.

What is tan on the unit circle?

Instead, think that the tangent of an angle in the unit circle is the slope. If you pick a point on the circle then the slope will be its y coordinate over its x coordinate, i.e. y/x. So at point (1, 0) at 0° then the tan = y/x = 0/1 = 0.

What is the unit circle and what is it used for?

In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

Where is Cos positive?

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.

How many radians are there in a circle?

Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees. The relation can be derived using the formula for arc length. Taking the formula for arc length, or . Assuming a unit circle; the radius is therefore one.

What is the difference between a degree and radian?

The angles of a triangle, on the other hand, are equal to 180 degrees. The radius of a circle is one-half of the distance across its center which makes an angle equal to one radian. A radian is equal to 180 degrees because a whole circle is 360 degrees and is equal to two pi radians.

How do you find the period?

If your trig function is either a tangent or cotangent, then you’ll need to divide pi by the absolute value of your B. Our function, f(x) = 3 sin(4x + 2), is a sine function, so the period would be 2 pi divided by 4, our B value.

What is sin to the negative 1?

The inverse sin of 1, ie sin-1 (1) is a very special value for the inverse sine function. Remember that sin-1(x) will give you the angle whose sine is x . Therefore, sin-1 (1) = the angle whose sine is 1.

What is cot to?

The trig function cotangent, written cot θ. cot θ equals or . For acute angles, cot θ can be found by the SOHCAHTOA definition, shown below on the left. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. f(x) = cot x is a periodic function with period π.

How do you find tan?

Example

  • Step 1 The two sides we know are Opposite (300) and Adjacent (400).
  • Step 2 SOHCAHTOA tells us we must use Tangent.
  • Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
  • Step 4 Find the angle from your calculator using tan-1
  • What is the Pythagorean identity?

    The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. (Note that sin2 θ means (sin θ)2).

    What is the sin of 0?

    (1, 0) = (x, y) = (cos 0, sin 0), cos 0 = 1, sin 0 = 0. The values of angles outside Quadrant I can be computed using reference angles, and the values of the other trigonometric functions can be computed using the reciprocal and quotient identities.

    What is the angle of reference?

    Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

    What is the Cotangent?

    Cosecant, Secant, and Cotangent. In addition to sine, cosine, and tangent, there are three other trigonometric functions you need to know for the Math IIC: cosecant, secant, and cotangent. These functions are simply the reciprocals of sine, cosine, and tangent. Cosecant. Cosecant is the reciprocal of sine.

    What does co terminal mean?

    Definition of coterminal. : having different angular measure but with the vertex and sides identical —used of angles generated by the rotation of lines about the same point in a given line whose values differ by an integral multiple of 2π radians or of 360° coterminal angles measuring 30° and 390°

    What is the reference angle of 240 degrees?

    A 240-degree angle is between 180 and 270 degrees, so its terminal side is in QIII. Subtract 180 from 240. You find that 240 – 180 = 60, so the reference angle is 60 degrees.

    What is the value of cos 60?

    Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees. I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0 , 30 , 45 , 60 and 90 .

    What is the meaning of theta?

    Most often, θ is a variable that stands for an angle in geometry, e.g.: Generally, φ represents longitude and θ represents latitude, though the choice is arbitrary. Often, two angles in the same plane are represented by α and β. Theta has many other uses.

    What is the tangent of 0?

    So let’s take a closer look at the sine and cosines graphs, keeping in mind that tan(θ) = sin(θ)/cos(θ). The tangent will be zero wherever its numerator (the sine) is zero. This happens at 0, π, 2π, 3π, etc, and at –π, –2π, –3π, etc.

    What is CSC?

    A Common Service Center (CSC) is an information and communication technology (ICT) access point created under the National e-Governance Project of the Indian government. The project plan includes the creation of a network of over 100,000 CSCs throughout the country.

    What are the two special right triangles?

    A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°.

    What are the inverse trig functions?

    Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle’s trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.