Find the value of cos(-225).
cos(-225°) is coterminal with cos 135°
By the CAST rule, cos 135° = -cos 45°
= -1/√2 or -√2/2
cos(-x) = cos(x)
cos(x-180) = -cos(x)
See if that helps you.
Or, draw the triangle in standard position, and recall that
cos(x) = x/r
Explain me in terms of unit circle.
Ok
Going either -225° or 135°, you would end up in the same position, right?
Now draw you 1 unit radius at 135 and sketch your right-angled triangle.
You have a right-angled triangle with a base and height of √2.
the value of x = -√2 and the the value of y is +√2
cos -225 = cos 135 = x/r = -√2/2
To find the value of cos(-225), we can use the trigonometric identity that states that the cosine function is an even function. This means that cos(-x) = cos(x) for any angle x.
Since we know that cos(-225) is equal to cos(225), we can determine the value of cos(225) by using the unit circle or a calculator.
First, let's use the unit circle to find the cosine of 225 degrees:
1. Draw a unit circle (a circle with a radius of 1 unit).
2. Locate the angle of 225 degrees on the unit circle.
3. The x-coordinate of the point where the angle intersects the unit circle is the value of cos(225).
4. Based on the unit circle, the point is located in the third quadrant, making the angle in standard position be 225 degrees.
5. In the third quadrant, the x-coordinate is negative, so cos(225) = -√2/2 or approximately -0.7071.
Alternatively, you can use a calculator to find the value of cos(225):
1. Ensure that your calculator is set to degrees mode.
2. Enter 225 and find the cosine function (cos) using the calculator.
3. The result should be -√2/2 or approximately -0.7071.
Therefore, the value of cos(-225) is also -0.7071 or -√2/2.