Question

answer questions 3, 4 and 5 using the following information. 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. 3 multiple choice 1 point a is 63.3 137.5 143.2 55.2 4 multiple choice 1 point b is 90 45 270 180 5 multiple choice 1 point k is an integer a whole number a multiple of 45 a multiple of 10

Explanation:

Step1: Find the reference angle

We know that \(\tan\theta = 1.99\). Using the inverse - tangent function \(\theta=\arctan(1.99)\).
\(\theta=\arctan(1.99)\approx63.3^{\circ}\) (using a calculator). The tangent function has a period of \(180^{\circ}\). The general form of the solutions for \(\tan\theta = \tan\alpha\) is \(\theta=\alpha + k\cdot180^{\circ}\), where \(k\in\mathbb{Z}\) ( \(k\) is an integer).

Step2: Analyze the options for \(a\), \(b\), and \(k\)

• For \(a\): The reference angle \(\alpha\approx63.3^{\circ}\), so \(a = 63.3\) (matches the first option in question 3).
• For \(b\): Since the period of the tangent function \(y = \tan x\) is \(T = 180^{\circ}\), so \(b = 180\) (matches the fourth option in question 4).
• For \(k\): In the formula \(\theta=a + bk\) (where \(\theta\) is the angle with \(\tan\theta=1.99\)), \(k\) is an integer (matches the first option in question 5).

Answer:

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