Can someone help explain why sin(30°) = sin(150°)

[ashxskyy]

Can someone help explain why sin(30°) = sin(150°)

Hi all! I am new here and found this forum by searching for places I could turn to if I needed help with my trig class. I happen to be pretty bad at it lol. I am looking forward to participating in the community! I'm having a really hard time getting this one:
Can someone explain why sin(30°) = sin(150°) (or

). Refer to both the unit circle and the graph of the sine curve. Give as much detail as you can.

 

[tkhunny]

Hi all! I am new here and found this forum by searching for places I could turn to if I needed help with my trig class. I happen to be pretty bad at it lol. I am looking forward to participating in the community! I'm having a really hard time getting this one:
Can someone explain why sin(30°) = sin(150°) (or

). Refer to both the unit circle and the graph of the sine curve. Give as much detail as you can.

Did you use your hint? The Unit Circle can be quite instructive.

Think "Reference Angle" or maybe think about the Vertical Distance from the x-Axis.

 

[Harry_the_cat]

Hi all! I am new here and found this forum by searching for places I could turn to if I needed help with my trig class. I happen to be pretty bad at it lol. I am looking forward to participating in the community! I'm having a really hard time getting this one:
Can someone explain why sin(30°) = sin(150°) (or

). Refer to both the unit circle and the graph of the sine curve. Give as much detail as you can.

Unit circle:
1. Draw a unit circle (centre (0,0) and radius 1).
2. Remembering that angles are measured anticlockwise from the positive x-axis, draw an angle of 30 degrees (starting at the origin).
3. This ray will cut the unit circle at a point. Sine of the angle is defined as the y-coordinate of this point.
4. Now do the same for 150 degrees (it will be in the second quadrant). Look at the point where this ray cuts the unit circle.
5. Because of symmetry, the y-coordinates of both these points are the same. Can you see that?
6. Therefore, because of the definition of sine, sin (30degrees) = sin (150 degrees).

Graph of sine curve:
1. Draw the sine curve on a normal set of axes (this curve can be derived from the unit circle by the way)
2. Just look at the part of the curve between 0 and 180 degrees. Symmetrical, isn't it.
3. So if you come in 30 degrees (to the right) from 0, and come in 30 degrees (to the left) from 180 (ie 150), the height of the sine curve will be the same. Can you see that?
4. So, again,

sin (30degrees) = sin (150 degrees).

In general, sin (180 - x) = sin x.

Hope that helps!​

 

[Steven G]

Hi all! I am new here and found this forum by searching for places I could turn to if I needed help with my trig class. I happen to be pretty bad at it lol. I am looking forward to participating in the community! I'm having a really hard time getting this one:
Can someone explain why sin(30°) = sin(150°) (or

). Refer to both the unit circle and the graph of the sine curve. Give as much detail as you can.

I think that you do not understand what this forum is about. You, the student, needs to give us as much detail as you can. Can you please graph the sine curve and point out where 150⁰ and 30^o are on the graph. Can you please draw both a 150⁰ and 30^o angle on the x-y plane and then complete the two right triangles. Try to label as much as you can on the triangles. Then please get back to us with your work.