MATH SOLVE

2 months ago

Q:
# Find the sine, cosine, and tangent of 120 degrees. (5 points) Sin 120 degrees = square root of 3 divided by 2, cos 120 degrees = negative 1 divided by 2, tan 120 degrees = negative square root of 3 Sin 120 degrees = negative 1 divided by 2, cos 120 degrees = square root of 3 divided by 2, tan 120 degrees = negative square root of 3 Sin 120 degrees = square root of 3 divided by 2, cos 120 degrees = 1 divided by 2, tan 120 degrees = square root of 3 Sin 120 degrees = square root of 3 divided by 2, cos 120 degrees = negative 1 divided by 2, tan 120 degrees = negative square root of 3

Accepted Solution

A:

120° will be found on in the second quadrant of the unit circle. Specifically, the reference angle will be 60°. This is because the angle measurement starts from the positive x axis, and rotates 120° counter-clockwise. The angle formed at this point between the line and the x-axis (negative direction) is 60°.

The special right triangle formed will have a hypotenuse of 1, and a reference angle of 60°.

We know that the adjacent line, the line opposite the 30° angle, will be 1/2 the hypotenuse, or -1/2. Negative because it goes in the negative x direction.

The opposite end, or vertical side, will be √3/2.

sin(120) = opposite/hypotenuse = √3/2 ÷ 1 = √3/2

cos (120) = adjacent/hypotenuse = (-1/2) / 1 = -1/2

tan (120) = opposite / adjacent = (√3/2) / (-1/2) = -√3

The special right triangle formed will have a hypotenuse of 1, and a reference angle of 60°.

We know that the adjacent line, the line opposite the 30° angle, will be 1/2 the hypotenuse, or -1/2. Negative because it goes in the negative x direction.

The opposite end, or vertical side, will be √3/2.

sin(120) = opposite/hypotenuse = √3/2 ÷ 1 = √3/2

cos (120) = adjacent/hypotenuse = (-1/2) / 1 = -1/2

tan (120) = opposite / adjacent = (√3/2) / (-1/2) = -√3