What are the Standard Angles of Trigonometric Table?
The Trigonometric Table is essentially a tabular compilation of trigonometric values and ratio for various conventional angles such as 0°, 30°, 45°, 60°, and 90°, often with extra angles such as 180°, 270°, and 360° included. Due to the existence of patterns within trigonometric ratios and even between angles, it is simple to forecast the values of the trigonometry table and to use the table as a reference to compute trigonometric values for many other angles. The sine function, cosine function, tan function, cot function, sec function, and cosec function are trigonometric functions.
The trigonometric table is helpful in a variety of situations. It is required for navigating, research, and architecture. This table was widely utilized in the pre-digital age, even before pocket calculators were available. The table also aided in the creation of the earliest mechanical computing machines. The Fast Fourier Transform (FFT) algorithms are another notable application of trigonometric tables.
Standard Angles of Trigonometric Table
The values of trigonometric ratios for the angles 0°, 30°, 45°, 60°, and 90° are widely utilized to answer trigonometry issues. These values are related to measuring the lengths and angles of a right-angle triangle. Hence, the standard angles in trigonometry are 0°, 30°, 45°, 60°, and 90°. Following are the trigonometry angle tables (show the figure).
The trigonometric table in its simplest sense refers to the collection of values of trigonometric functions of various standard angles including 0°, 30°, 45°, 60°, 90°, along with other angles such as 180°, 270°, and 360°. These angles are all included in the table. This makes it easier to determine and arrive at the values of the trigonometric ratios in a trigonometric table, also, the table can be used as a referral illustration to compute trigonometric values for various other angles, due to the patterns that are seen within the trigonometric ratios and those between angles.
The table as one might note, consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent. The short forms of these are very popular – sin, cos, tan, cosec, sec, and cot, respectively. Always, memorize the values of the trigonometric ratios of the standard angles.
Always remember these points in the trigonometric table:
In a trigonometric table, the trigonometric values for complementary angles, such as 30° and 60° are measured by applying complementary formulas for various trigonometric ratios.
The value for some ratios in a table is ∞ “not defined”. The reason is that while computing values, the denominator shows a “0”, which implies that the trigonometric value cannot be defined, and is as good to be the equivalent of infinity.
Please notice the sign change in the values at places under 180°, and 270°, for values of some trig ratios in a trigonometric table. This happens because there is a change in the quadrant.
Trigonometric values
As explained, if trigonometry deals with the relationship between the sides of a triangle (right-angled triangle) and its angles, then the trigonometric value refers to the values of different ratios, sine, cosine, tangent, secant, cotangent, and cosecant, all in the trigonometric table. All the trigonometric ratios are in relation with the sides of a right-angle triangle. The trigonometric values are derived applying these the ratios. Refer to the following steps to create trigonometric values:
Steps to Create Values for Trigonometry Table
Step 1:
Make a table with the top row showing the angles such as 0°, 30°, 45°, 60°, and 90°, and the first column listing the trigonometric functions such as sin, cos, tan, cosec, sec, cot.
Step 2: Determine the value of sin
To find the sin values, divide 0, 1, 2, 3, 4 by 4 under the root, in that order.
Step 3: Determine the value of cos
The cos-value is the inverse of the sin angle. To find the value of cos, divide by 4 in the opposite order as sin.
Step 4: Determine the value of tan
Tan is defined as sin divided by cos. Tan equals sin/cos. Divide the value of sin at 0° by the value of cos at 0° to get the value of tan at 0°.
Step 5: Determine the value of cot
The reciprocal of tan is the value of cot. Divide 1 by the value of tan at 0° to get the value of cot at 0°. As a result, the value will be as follows: cot 0° = 1/0 = Unlimited or Not Defined
Step 6: Determine the value of cosec
The reciprocal of sin at 0° is the value of cosec at 0°.
Step 7: Determine the value of sec
Any common values of cos may be used to calculate sec. The value of sec on 0° is the inverse of the value of cos on 0°.
While we learn trigonometric values of the trigonometry tables, it will also be interesting to take note of the application areas of the table. On a broader note, the trigonometric table is used in:
Science, technology, engineering, navigation, science and engineering. Before the advent of the digital era, the trigonometric table was very effective. In the course of time, the table helped in the conceptualization of mechanical computing devices. Trigonometric tables are also used in the Fast Fourier Transform (FFT) algorithms.
Important Tricks to Remember Trigonometry Table
Knowing the trigonometry table can help you answer trigonometry problems and remembering the trigonometry table for normal angles ranging from 0° to 90° is simple. Knowing the trigonometric formulae makes remembering the trigonometry table much easier. The trigonometry formulae are required for the Trigonometry ratios table.
The angle values of trigonometric functions, cotangent, secant, and cosecant are computed by applying these standard angle values of sine, cosecant, and tangent. All the higher angle values of trigonometric functions such as 120°, and 360°, are easier to compute, through the standard angle values in a trigonometric values table.
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