Trigonometric Ratios of Standard Angles

What are Trigonometric Ratios?

The trigonometric ratios of an angle are the ratios of the lengths of the sides of the triangle formed by the angle, with the longest side taken as the hypotenuse. The most common ratios are sine, cosine, and tangent. Trigonometric Ratios of Standard Angles.

What is Sin, Cos and Tan?

Sine, cosine, and tangent are all functions that relate angles and distances in a right triangle. The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

The Different Values of Sin, Cos and Tan concerning Radians have been Listed Down in the Table Given Below

Sine, Cosine, Tangent Values in Radians

Sine, Cosine, Tangent Values in Radians Sin Cos Tan 0 0 0 1 0.5 0.7142 2 0.8661 0.5 2.6609 3 0.9842 0.3333 3.4142 4 1.0 0.25 4.0 5 1.0476 0.2 5.0476 6 1.0551 0.1666 6.0551 7 1.0643 0.1428 7.0643 8 1.0729 0.125 8.0729 9 1.0816 0.1111 9.0816 10 1.0903 0.1 10.0903

Derivation of Values of Trigonometric Standard Angles

The values of the trigonometric standard angles are derived from the properties of right triangles.

The sine of a right angle is 1, and the cosine and tangent of a right angle are both 0.

The sine, cosine, and tangent of other angles can be found using the following formulas:

sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent

Here are Values of the Trigonometry Standard Angles

There are six trigonometry standard angles: 30°, 45°, 60°, 90°, 120°, and 180°.

Here are Values of the Trigonometry Standard Angles

The values of the trigonometry standard angles are:

30 degrees
45 degrees
60 degrees
90 degrees
180 degrees

Here are Values of the Trigonometry Standard Angles

The trigonometry standard angles are 0, 30, 45, 60, and 90 degrees.

Here is the Standard Angles Table

Standard angles are measure in degrees. There are 360 degrees in a full circle.

There are also standard angles that are used in construction. These angles are usually measured in radians. There are 2π radians in a full circle.

Here is the Standard Angles Table

Standard angles are angles that are used as a basis for measurements. There are a number of standard angles, including the right angle, the acute angle, and the obtuse angle.

Some angles are standard angles. These angles are used in many different situations.

There are a few standard angles that are used in many different situations. These angles are:

0 degrees
45 degrees
90 degrees
180 degrees

Table Showing the Value of Each Ratio with Respect to Different Angles

The table below shows the value of each ratio with respect to different angles.

Ratio Value with Respect to Angle 0° 45° 60° 90° 120° 135° 150° 1 1 1 1 1 1 1 1 2 1.414 1.5 1.6 1.7 1.8 1.9 2 3 2.0 2.1 2.2 2.3 2.4 2.5 4 2.667 2.8 2.9 3.0 3.1 3.2 3.3 5 3.333 3.5 3.6 3.7 3.8 3.9 4

As the angle changes, the value of the ratios also change.

( Trigonometric Ratios of Standard Angles Table)

Angle (degrees) Sin θ Cos θ Tan θ Sec θ Csc θ 0 0 1 1 0 0 90 0.866 0.5 0.5 1.73 0.5 3.14 180 0.5 -0.5 0 0 1 1 270 -0.5 0.866 -1 -1 0 0

Few Applications of Trigonometry

Some specific applications of trigonometry include determining distances between points, plotting ship routes, surveying land, and modeling the movement of celestial objects. Additionally, trigonometry is also used extensively in the fields of engineering and physics.

Questions to be Solved

1) What is the wavelength of the blue light emitted from a hydrogen atom when it goes from the n=2 to the n=1 energy level?

2) What is the energy difference between the n=2 and the n=1 energy levels in a hydrogen atom?

3) What is the frequency of the blue light emitted from a hydrogen atom when it goes from the n=2 to the n=1 energy level?