The cosine function of an angle follows a particular formula. According to this formula, the value of a cosine function of an angle is the length of the adjacent side divided by the length of the hypotenuse side. The formula is written below. There are three basic trigonometric ratios, and they are sine function, cosine function, and tangent function.
With the help of the sin, cos, and tan functions, the angles of a triangle can be calculated. For understanding the cosine function of an acute angle, you need to draw a right-angled triangle on a piece of paper.
The triangle obviously has three sides, and these sides can be defined in the following way:. Notably, this is the longest side of a right-angle triangle. The process starts with assuming a unit circle which shares its center with the origin of the coordinate axes. Thus, mathematically it is written in the following form in trigonometry i. Practice: Solve sinusoidal equations basic.
Practice: Solve sinusoidal equations. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Instructor] In the graph below, for what values of theta does cosine of theta equal one, and for what values of theta does cosine of theta equal negative one? And they've very nicely graphed it for us, the horizontal axis is the theta axis, and the vertical axis is the y-axis, and so this is the graph of y is equal to cosine of theta.
And it makes sense with a unit circle definition, and I'll just make sure that we're comfortable with that, because with our unit circle definition, so let me draw ourselves a unit circle, and I'm just going to draw it very roughly, just so that we get the general idea of what's going on here. When theta is equal to zero, we're at this point right over here on the unit circle. Well what's the x-coordinate of that point? Well it's one, and you see when theta's equal to zero, on this graph, cosine of theta is equal to one.
When theta is equal to pi over two, we're at this point on the unit circle, and the x-coordinate is what? Well, the x-coordinate there is zero. And you see once again, when we're at pi over two, the x-coordinate is zero, so this is completely consistent with our unit circle definition.
As we move in the rightward direction, we're moving counterclockwise around the unit circle, and as we move in the leftward direction, we're moving counter, sorry. If we move in the rightward direction, we're moving counterclockwise, and as we're moving in the leftward direction along the axis in the negative angles, we're moving in the clockwise, we're moving in the clockwise direction around our unit circle. So let's answer their question. For what values of theta does cosine of theta equal one?
Well we can just read the graph right over here. It equals one, so cosine of theta equals one, cosine of theta equals one at, at theta is equal to, well, we see it right over here.
Theta is equal to zero, theta is equal to, well we've gotta go all the way again to two pi, two pi, but then it just keeps going on and on, and it makes sense. Theta equaled, or sorry, cosine of theta, the x-coordinate on this unit circle equaled one right when we were at zero angle, and we had to go all the way around the circle to get back to that point, two pi radians. But then it'll be again when we get to four pi radians, and then six pi radians, so two pi, four pi, six pi, and I guess you could see the pattern here.
We're gonna keep hitting cosine of theta equals one every two pi, so you could really kind of view this as every multiple of two pi. Two pi n, where n is an integer, n is integer And that applies also for negative values.
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