Use a calculator to determine angle x, rounded
to the nearest degree.
a) csc x 1.25
b) sec x _
12
7
c) cot x 3.1416
d) sec x 1.32
a) To solve for angle x using the given equation csc x = 1.25, we need to take the inverse of the cosecant function (also known as the arcsine function) of 1.25.
Using a calculator, find the inverse sine (arcsine) of 1.25 by entering "1.25" followed by "sin^-1" or "arcsin".
The calculator will give you the result: 51.32 degrees.
So, angle x is approximately 51 degrees (rounded to the nearest degree).
b) To solve for angle x using the given equation sec x = 12/7, we need to take the inverse of the secant function (also known as the arccosine function) of 12/7.
Using a calculator, find the inverse cosine (arccosine) of 12/7 by entering "12/7" followed by "cos^-1" or "arccos".
The calculator will give you the result: 25.41 degrees.
So, angle x is approximately 25 degrees (rounded to the nearest degree).
c) To solve for angle x using the given equation cot x = 3.1416, we need to take the inverse of the cotangent function (also known as the arctangent function) of 3.1416.
Using a calculator, find the inverse tangent (arctangent) of 3.1416 by entering "3.1416" followed by "tan^-1" or "arctan".
The calculator will give you the result: 72.343 degrees.
So, angle x is approximately 72 degrees (rounded to the nearest degree).
d) To solve for angle x using the given equation sec x = 1.32, we need to take the inverse of the secant function (also known as the arccosine function) of 1.32.
Using a calculator, find the inverse cosine (arccosine) of 1.32 by entering "1.32" followed by "cos^-1" or "arccos".
The calculator will give you the result: 44.189 degrees.
So, angle x is approximately 44 degrees (rounded to the nearest degree).