Why does sin 30 degress (math term) equal to cos 60 degress (math term)?

Question

Can anyone help me with this math problem. List any instructions or a picture. If so please explain your point in simple terms

Answer 1

look at the unit circle. sin is y and cos is x.
look at the circle, 30 degree is (root3/2, 1/2)
and 60 degree is (1/2, root3/2), since sin is y, so sin 30 = 1/2.
and cos is x, so cos 60 = 1/2.

Answer 2

There are 2 ways to explain this.

1. Do you know what the unit circle is? Here is a picture in case you dont - http://dcr.csusb.edu/LearningCenter/LCimages/UnitCircle.gif . The coordinates for 30 degrees are ( sqroot of3 divided by 2, 1/2). Sine of that would be the y value, meaning 1/2. The coordinates for 60 degrees are (1/2, sqroot of 3 divided by 2). Cosine of 60 degrees would be the x value, or 1/2.

2. If you have a right triangle ABC, lets say that C is the right angle, A is 30 degrees, and B is 60 degrees. In a right triangle, the sine of an angle is opposite over hypotenuse. If the side opposite angle A is a, and the hypotenuse is c, and the side opposite angle B is b, then sin A = sin 30 degrees = a/c . Cosine is adjacent over hypotenuse. cos B = cos 60 degrees = a/c.

Hope this helps!

Answer 3

If you draw a right angle triangle with one angle 30 degrees then the third angle will be 60 degrees.

Let triangle be ABC A=30 B=60 C=90. Hypotenuse opposite R/A running from 30 to 60 degrees.(A to B)

So side AC from one point of view is cos 30 and the other angle sin 60. Draw this triangle and it should be obvious.

Cos is adjacent/hypoteneuse
Sin opposite/hypoteneuse

Answer 4

Because sin is Opposite/Hypotenuse and cos in Adjacent/Hypotenuse.

In a 30 60 90 triangle, the side opposite the 30 is x, the side opposite the 60 is x(sqrt)3, and the side opposite the 90 is 2x.
Sin 30= x/2x or 1/2
Cos 60= x/2x or 1/2

Answer 5

When you place a 30 degree angle with vertex at the origin, the place on the unit circle where is crosses, the y value = 1/2. The 60 degree angle placed at the origin, the x value = 1/2. Since the x axis represents cosine and the y axis sine for the unit circle, the values are equal.

Answer 6

Sin 30 Degrees

Answer 7

Sine and Cosine are just ratios of the sides of any right triangle. Sine is the ration of the side opposite the given angle over the hypotenuse of the triangle. Cosine is the side adjacent over the hypotenuse. In a 30-60-90 triangle, these ratios just happen to describe the same sides. Try drawing it out.

Answer 8

A.........................B 30
|
|
C 60
The figure above represents a 30-60-90 right triangle. The side adjacent to the 60 degree angle is AC. The side opposite the 30 degree angle is also AC.
The hypotenuse is BC (which is hard to show).
cos 60 = adj./hypot. = AC/BC
sin 30 = opp./hypot. = AC/BC

Answer 9

cosine It is used with triangles and with the unit circle. Basically, if you have a circle with a diameter of 1 with the origin as its center, so that it intersects the x and y axes at both -1 and 1, the cosine of an angle refers to what its x coordinate would be. It must lie betwee -1 and 1 (inclusive).

Answer 10

sin A = cos (90° – A)
cos A = sin (90° – A)