How do you find the exact value of sin(0)?

1 Answer
Noah G
Aug 22, 2016

sin0˚ = 0

Explanation:

By the unit circle:

![https://www.mathsisfun.com/geometry/http://unit-circle.html](https://useruploads.socratic.org/D5fjZeDNR86pXbI8MJSN_circle-unit-304560.gif)

As you can see, pairs are ordered in the manner of (cos,sin). In other words, the x value is cos and the y value is sin.

Since in this problem we're dealing with the sine function, you can ask yourself: What is the y-value at 0˚?

Well, the point at 0˚ is (1, 0), and the y value here is 0. The hypotenuse, although measuring 1 unit, doesn't matter, because 0/a, a != 0, always equals 0, no matter the value of a. Hence, sin0˚ = 0.

Practice exercises:

1. Find the values of the variables in the following blank unit circle.

![https://www.pinterest.com/pin/77616793549234244/ with adaptations](useruploads.socratic.org)

2. Determine the following exact values:

a) sin240˚

b) cos(pi/2)

c) tan((7pi)/6)

Hopefully this helps, and good luck!

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