Question

The reference angle for 305° is _____°

If the point p(-3/5, y) lies on the unit circle and P is in the second quadrant, what does y equal? If necessary, use the slash mark (/) for a fraction bar.

Answer:_________


What are the coordinates of the terminal point determined by t = 20π /3

A: (½, √3/2)
B: (-1/2, √3/2)
C: (½, -√3/2 )
D: (-1/2, -√3/2)

Answer 1

Answer on Question #57981 – Math – Trigonometry

Question

Reference angle for $305{}^{\circ}$ is ___°.

Solution

$305{}^{\circ}$ is in the $4^{\text{th}}$ quadrant, so

$$x = 360{}^{\circ} - 305{}^{\circ} = 55{}^{\circ}$$

**Answer:** $55{}^{\circ}$

Question

If the point $p(-3/5, y)$ lies on the unit circle and $P$ is in the second quadrant, what does $y$ equal? If necessary, use the slash mark (/) for a fraction bar.

Solution

Because the point $p(-3/5, y)$ lies on the unit circle, it follows that

$$\left(- \frac {3}{5}\right) ^ {2} + y ^ {2} = 1,$$

hence

$$y = \sqrt {1 - \left(\frac {3}{5}\right) ^ {2}},$$ $$y = \pm \frac {4}{5},$$

Given $P$ is in the second quadrant, hence we take

$$y = \frac {4}{5}$$

**Answer:** $y = 4 / 5$

Question

What are the coordinates of the terminal point determined by $t = 20\pi /3$

Solution

$$x = \cos \frac {20\pi}{3} = \cos \left(6\pi + \frac {2\pi}{3}\right) = \cos \frac {2\pi}{3} = - \frac {1}{2},$$ $$y = \sin \frac {20\pi}{3} = \sin \left(6\pi + \frac {2\pi}{3}\right) = \sin \frac {2\pi}{3} = \frac {\sqrt {3}}{2}.$$

Answer: B: (-1/2, √3/2).

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