Question

Using what you know about the sin 330, how would you find the value of sin 330 using a triangle and not a calculator?"

A.) From a triangle, I would then find what is ((square root of 2/2
B.) From a triangle, I would then find what is -1/2 / 1
C.) From a triangle, I would then find what is 1/ (( negative square root of 3/ 2

Answer 1

To find the value of sin 330 using a triangle, you can use the trigonometric identity sin(A + B) = sin A cos B + cos A sin B. In this case, A = 300 and B = 30, so sin 330 = sin(300 + 30) = sin 300 cos 30 + cos 300 sin 30. Using a 30-60-90 triangle, where sin 30 = 1/2 and cos 30 = √3/2, we can substitute these values into the trigonometric identity to find sin 330: √3/2.

Step-by-step explanation:

To find the value of sin 330 using a triangle, you can use the trigonometric identity sin(A + B) = sin A cos B + cos A sin B. In this case, A = 300 and B = 30, so sin 330 = sin(300 + 30) = sin 300 cos 30 + cos 300 sin 30.

Using a triangle, we can construct a 30-60-90 triangle where the side opposite the 30 degree angle is 1, the side opposite the 60 degree angle is √3, and the hypotenuse is 2. From this triangle, we can find that sin 30 = 1/2 and cos 30 = √3/2.

Now we can substitute these values into the trigonometric identity to find sin 330: sin 330 = sin(300 + 30) = sin 300 cos 30 + cos 300 sin 30 = (√3/2)(1/2) + (1/2)(√3/2) = √3/4 + √3/4 = (2√3)/4 = √3/2.