About Arctan Formula
In trigonometry, the arctan formula is the inverse of the tangent function, which is defined as the ratio of the opposite side to the adjacent side at a certain angle of a right-angled triangle. tan-1 is another name for Arctan. The arctan formula is presented here, along with illustrations.
What is Arctan Formula?
The basic arctan formula will be written as:
θ=arctan(opposite / adjacent)
Example based on Arctan Formula
Examples Using Arctan Formula:
Examples1 In a right-angled triangle DEF, if the base of the triangle is 34 and the height is 22. Find the base angle.
Solution:
To find: θ
Using the arctan formula,
θ=arctan(opposite / adjacent)
θ=arctan(22/34)=0.57430483
Answer: Therefore, θ = 32.998o.
Examples2 In a right-angled triangle XYZ, if the base of the triangle is 4 and the height is 3. Find the base angle.
Solution:
To find: θ
Using the arctan formula,
θ=arctan(opposite /adjacent)
θ=arctan(3/4)=0.64350110
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Frequently Asked Questions
The arctan formula is widely used in engineering, physics, and computer graphics for determining angles in navigation, calculating slopes in road design, and adjusting camera perspectives in 3D modeling.
The arctan formula, also known as the inverse tangent function, is expressed as:
y=tan-11(x)
This function finds the angle y whose tangent is x. It is widely used in trigonometry, calculus, and physics for solving right-angle triangles and analyzing slopes.