i. write true if the statement or equation is always true. otherwise, write false. 5 pts 1. the angle…

i. write true if the statement or equation is always true. otherwise, write false. 5 pts 1. the angle measure of 2 radians is equivalent to 360°. 2. an angle in the standard position is in quadrant i. 3. -130° is coterminal with 230°. 4. point p (\\(\\frac{1}{4},-\\frac{1}{3}\\)) is in the unit circle. 5. in quadrant iii, the tangent function is negative.

i. write true if the statement or equation is always true. otherwise, write false. 5 pts 1. the angle measure of 2 radians is equivalent to 360°. 2. an angle in the standard position is in quadrant i. 3. -130° is coterminal with 230°. 4. point p (\\(\\frac{1}{4},-\\frac{1}{3}\\)) is in the unit circle. 5. in quadrant iii, the tangent function is negative.

Answer

Explanation:

Step1: Analyze statement 1

We know that (1) radian (=\frac{180^{\circ}}{\pi}\approx57.3^{\circ}). Then (2) radians (=2\times\frac{180^{\circ}}{\pi}\approx 114.6^{\circ}\neq360^{\circ}).

Step2: Analyze statement 2

Angles in standard position: Quadrant I: (0^{\circ}<\theta < 90^{\circ}) or (0 <\theta<\frac{\pi}{2}) radians. An angle in standard position is not in Quadrant I. For example, (120^{\circ}) is in Quadrant II.

Step3: Analyze statement 3

Coterminal angles: (\theta_{1}=\theta_{2}+360^{\circ}n), (n\in\mathbb{Z}). Let (\theta_{1}=- 130^{\circ}) and (\theta_{2}=230^{\circ}). Then (-130^{\circ}=230^{\circ}+360^{\circ}n). Solving for (n): (-130 - 230=360n), (-360 = 360n), (n=-1).

Step4: Analyze statement 4

For a point (P(x,y)) on the unit circle (x^{2}+y^{2}=1). If (x = \frac{1}{4}) and (y=-\frac{1}{3}), then (x^{2}+y^{2}=\left(\frac{1}{4}\right)^{2}+\left(-\frac{1}{3}\right)^{2}=\frac{1}{16}+\frac{1}{9}=\frac{9 + 16}{144}=\frac{25}{144}\neq1).

Step5: Analyze statement 5

In Quadrant III, (x<0) and (y < 0). The tangent function (\tan\theta=\frac{y}{x}). Since (x<0) and (y < 0), (\tan\theta=\frac{y}{x}>0).

Answer:

  1. False
  2. False
  3. True
  4. False
  5. False