Determine the exact expression for the following.
- cos(pi/4)=(x/60)
I got x=60/√2 Is that correct?
Also, I had a lot of trouble with this one:
cos(pi/6)=(z/60)
I got z=(√3 (60/√2))/2
That doesn't seem right, but I don'r know what I', doing wrong. Also, I used a unit circle to get the values for cos.
First one is ok
Second one:
cos(pi/6) = √3/2
so z = 60(√3/2) = 30√3
thank you so much! :)
To determine the exact expressions for the given cosine equations, you can use the unit circle and the trigonometric identities. Let's go through each question one by one.
1. cos(pi/4) = (x/60)
To find the value of x, we need to recall the value of cosine for the angle pi/4 (45 degrees) on the unit circle. At this angle, the x-coordinate of the point on the unit circle represents the cosine value.
From the unit circle, we can see that at pi/4, the x-coordinate is equal to √2/2. Therefore, we can set up the equation:
√2/2 = x/60
To solve for x, we can cross-multiply:
2x = 60 * √2
Dividing both sides by 2, we get:
x = 30 * √2
So, the correct expression for x is x = 30 * √2. Therefore, your answer of x = 60/√2 is not correct.
2. cos(pi/6) = (z/60)
To find the value of z, we need to recall the value of cosine for the angle pi/6 (30 degrees) on the unit circle. At pi/6, the x-coordinate represents the cosine value.
From the unit circle, we can see that at pi/6, the x-coordinate is equal to √3/2. Therefore, we can set up the equation:
√3/2 = z/60
To solve for z, we can cross-multiply:
2z = 60 * √3
Dividing both sides by 2, we get:
z = 30 * √3
So, the correct expression for z is z = 30 * √3. Therefore, your answer of z = (√3 (60/√2))/2 is not correct.
As a side note, it's important to be cautious when using a calculator for evaluations involving square roots. Make sure to use parentheses properly to avoid ambiguity in calculations.