Question

tangent angles
what are the measures of all of the angles that have a tangent value of 1.99? give
the answer in degrees rounded to the nearest tenth.
the measures of all the angles are a + bk.
choose the numbers to finish each sentence.
1 multiple choice 1 point
a is
143.2
137.5
55.2
63.3
2 multiple choice 1 point
b is
45
90
180
270
3 multiple choice 1 point
k is
a whole number
an integer
a multiple of 10
a multiple of 45

Explanation:

Step1: Find the reference angle

We know that if \(\tan\theta = 1.99\), then \(\theta=\arctan(1.99)\). Using a calculator, \(\arctan(1.99)\approx63.3^{\circ}\)

Step2: Determine the general form of the tangent function

The tangent function \(y = \tan x\) has a period of \(180^{\circ}\). The general solution for \(\tan\theta=\tan\alpha\) is \(\theta=\alpha + k\cdot180^{\circ}\), where \(k\in\mathbb{Z}\) ( \(k\) is an integer)

Answer:

1. \(63.3\)
2. \(180\)
3. an integer