How to Find the Y-Intercept in a Sine Graph

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The y intercept of a graph is the point where the line crosses the y-axis (the vertical one). This happens when x = 0. The sine is a trigonometric function. In a right triangle, the sine of an angle is the ratio of the side opposite the angle to the hypotenuse (the longest side). Like all trigonometric functions, sin(x) is cyclical.

Difficulty:Moderately Easy1

Decide if you want to use the graphical method or the algebraic method. If you are given a graph, use the graphical method and simply look for the point where the line crosses the y-axis. If you are given a formula, go to Step 2.

2

Write the formula for x = 0. For example, if your function is y = 2.5*sin(3x) + 21, write 2.5*sin(0) + 21.

3

Calculate the formula. Y = 2.5*sin(3*0) + 21 = 2.5*sin(0) + 21 = 2.5*0 + 21 = 21. (You can calculate the sine on a scientific calculator, or in Excel, or from a table). The y intercept is 21.

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