Find the exact value of cos 300 degrees.
thanks guys
cos 300 = 1/2 = 0.500
how do you know? I am supposed to show my work.
You ought to know the rule on 30-60-90 triangles. If the hyp is 2, the shorter side is 1, and the longer side is sqrt3.
what does that have to do with cos300?
Cos(x) = Cos(-x) (1)
Cos(x + 360) = cos(x) (2)
Cos(300) = (using (2)) cos(-60) = (using (1)) cos(60) = using what Bobpursley wrote above 1/2
where did you get 60 from?
Bill, the sixty came from the addition formula above. 300 + 60 = 360
Bob, it says Cos(x + 360) .
Cos(x + 360) = Cos(x)
substitute x = y - 360:
Cos(y - 360 + 360) = Cos(y - 360) --->
Cos(y) = Cos(y - 360)
Substitute y = 300:
cos(300) = cos(-60)
Where did you get substitute x = y - 360 from? I'm sorry, I am so confused. Do you think you could give me the formula or whatever and then show me how to plug in the 300, or is that what you are doing now?
I apologize for the confusion. Let me provide a clearer explanation.
To find the exact value of cos 300 degrees, we can use the unit circle.
The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. The measure of an angle is the length of the arc on the unit circle formed by the angle's terminal side.
For the angle 300 degrees, start at the positive x-axis (cos 0) and rotate counterclockwise 300 degrees. This brings you into the fourth quadrant of the unit circle.
In the fourth quadrant, the x-coordinate (cosine value) is positive and the y-coordinate (sine value) is negative. Since the cosine of an angle in the fourth quadrant is positive, we know that cos 300 degrees is positive.
Now, let's determine the reference angle. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. The reference angle for 300 degrees is 60 degrees.
We know that the cosine of an angle is equal to the x-coordinate of the point on the unit circle corresponding to that angle.
Using the reference angle of 60 degrees, we can find the exact value of cos 60 degrees. In a 30-60-90 right triangle (which is a special triangle), the ratio of the length of the shorter leg to the hypotenuse is 1/2. Therefore, the x-coordinate (cosine value) of the angle 60 degrees is 1/2.
Since cos 300 degrees is positive, the exact value of cos 300 degrees is 1/2.
To summarize:
Start at cos 0 degrees on the unit circle and rotate counterclockwise 300 degrees.
This brings you into the fourth quadrant where cosine is positive.
The reference angle for 300 degrees is 60 degrees.
In a 30-60-90 right triangle, the cosine of 60 degrees is 1/2.
Therefore, the exact value of cos 300 degrees is 1/2.