How do i do these inverse trig

Mathematics

2 answers:

jok3333 [9.3K]3 years ago

8 0

This is a right triangle
so
Cos x = 109 / 134 then x = cos⁻¹ (109/134) = 35.567°
sin y = 109 / 134 then y = sin⁻¹ (109/134) = 54.433°
and
the third side = √(134² - 109²) = 77.94

Fed [463]3 years ago

7 0

To do inverse trig functions on a calculator, enter the value and press either the arcsin, arccos and arctan buttons OR $sin^{-1}, cos^{-1}, tan^{-1}$ buttons. The functions arcsin(x), arccos(x) and arctan(x) are the inverse functions of the 3 main trigonometric functions sin(x), cos(x), and tan(x) formed by a reflection across the line y=x. This results in the (x,y) points of sin(x), cos(x) and tan(x) switching their order (y,x) in each inverse. Form a ratio of the side lengths, press the corresponding inverse function and you will find x = 35.6 degrees and y = 54.4 degrees.

<h3>Further Explanation </h3>

Sine/ Cosine/Tangent

In trigonometry, there are three main functions sine, cosine, and tangent based on the ratios of sides corresponding to angles within a right triangle. The ratio for sine is opposite / hypotenuse. The ratio for cosine is adjacent / hypotenuse. The ratio for tangent is opposite / adjacent.

Notice in this triangle, 109 and 134 are the adjacent and hypotenuse to the angle x. This is the cosine function and thus Cos(x) = 109 / 134. 109 and 134 are also the opposite and hypotenuse to the angle y. This is the sine function and thus sin y = 109 / 134. To solve for x and y, use the inverse function arcsin and arccos.

Arcsin

As the arcsin(x) is the inverse of the sin(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arcsin is the triangle side ratios (opposite / hypotenuse) and they align to the angle outputs of this function. For example, if sin (30) = 1/2 then arcsin(1/2) = 30. By pressing the arcsin button on your calculator it reverses the inputs and outputs. The expression sin y = 109/ 134 becomes arcsin (109/134) = y and y = 54.4 degrees.

Arccos

As the arccos(x) is the inverse of the cos(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arccos is the triangle side ratios (adjacent / hypotenuse) and they align to the angle outputs of this function. For example, if cos (60) = 1/2 then arccos(1/2) = 60. By pressing the arccos button on your calculator it reverses the inputs and outputs. The expression cox x = 109/ 134 becomes arccos (109/134) = x and x = 35.6 degrees.

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