What is the y-value at 330°? Write as an exact value (no decimal).(1 point)

Answer 1

To find the y-value at \( 330^\circ \), we can use the unit circle.

The angle \( 330^\circ \) is in the fourth quadrant, where the sine function (which corresponds to the y-coordinate) is negative.

The reference angle for \( 330^\circ \) is: \[ 360^\circ - 330^\circ = 30^\circ \]

The sine of \( 30^\circ \) is: \[ \sin(30^\circ) = \frac{1}{2} \]

Since \( 330^\circ \) is in the fourth quadrant, the y-value is negative: \[ \sin(330^\circ) = -\sin(30^\circ) = -\frac{1}{2} \]

Therefore, the y-value at \( 330^\circ \) is: \[ \boxed{-\frac{1}{2}} \]

Answer 2

What is the x-value at 150° ? Write as an exact value (no decimal).(1 point)

Answer 3

To find the x-value at \( 150^\circ \), we can refer to the unit circle.

The angle \( 150^\circ \) is in the second quadrant, where the cosine function (which corresponds to the x-coordinate) is negative.

The reference angle for \( 150^\circ \) is: \[ 180^\circ - 150^\circ = 30^\circ \]

The cosine of \( 30^\circ \) is: \[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]

Since \( 150^\circ \) is in the second quadrant, the x-value is negative: \[ \cos(150^\circ) = -\cos(30^\circ) = -\frac{\sqrt{3}}{2} \]

Therefore, the x-value at \( 150^\circ \) is: \[ \boxed{-\frac{\sqrt{3}}{2}} \]

Answer 4

Sorry the other day you told me it was -1/2

Answer 5

Let me clarify to make sure we have accurate information.

For \( 330^\circ \):

• The reference angle is \( 30^\circ \).
• The sine of \( 30^\circ \) is \( \frac{1}{2} \).
• Since \( 330^\circ \) is in the fourth quadrant, the sine value (y-value) is negative:

Hence, \[ \sin(330^\circ) = -\frac{1}{2} \]

So the y-value at \( 330^\circ \) is indeed: \[ \boxed{-\frac{1}{2}} \]

And for \( 150^\circ \):

• The reference angle is \( 30^\circ \).
• The cosine of \( 30^\circ \) is \( \frac{\sqrt{3}}{2} \).
• Since \( 150^\circ \) is in the second quadrant, the cosine value (x-value) is negative:

Therefore, \[ \cos(150^\circ) = -\frac{\sqrt{3}}{2} \]

So, the x-value at \( 150^\circ \) is: \[ \boxed{-\frac{\sqrt{3}}{2}} \]

To summarize:

• \( y \)-value at \( 330^\circ \) is \( -\frac{1}{2} \).
• \( x \)-value at \( 150^\circ \) is \( -\frac{\sqrt{3}}{2} \).

I hope this clears up any confusion! Please let me know if you have any other questions.