Determine the least positive value of t for which d=0.
d=cos((3pi/4)(t))
0=cos((3pi/4)(t))
I got stuck on this step
Please help
Cosine is 0 at pi/2
3pi/4*t=pi/2
t=2/3
Well, it seems like you're stuck on solving the equation 0 = cos((3π/4)(t)). Don't worry, I'm here to help (or at least try my best while attempting some humor)!
To find the least positive value of t for which d = 0, we need to solve the equation. In this case, we want the cosine function to equal zero.
Cosine is equal to zero at the following angles: π/2, 3π/2, 5π/2, and so on. So, we can set (3π/4)(t) equal to one of these angles:
(3π/4)(t) = π/2
Now, let's try to solve it with a little twist. Let's invite some clowns into the equation! Why not? After all, life is too serious sometimes.
So, we have:
(3π/4)(t) = π/2
Now, imagine a silly clown riding a unicycle, juggling pies, and trying to solve this equation. How hilarious! Now, let's get back to the problem.
We can solve the equation by dividing both sides by (3π/4):
t = (π/2) / (3π/4)
Simplifying further, we get:
t = 2/3
So, the least positive value of t for which d = 0 is t = 2/3. And now you know that clowns can solve equations too – but don't worry, their answers are just as accurate as any other method.
I hope that helps! Let me know if you need any further assistance, or if you'd like me to tell you more jokes.
To determine the least positive value of t for which d = 0, we need to solve the equation 0 = cos((3π/4)(t)).
To solve this equation, we need to find the values of t that make the cosine function equal to zero.
The cosine function equals zero when the angle inside the cosine function is equal to half of an odd multiple of π.
In other words, we need to solve the equation (3π/4)(t) = (2n + 1)(π/2), where n is an integer.
To get t by itself, we can divide both sides by (3π/4):
t = [(2n + 1)(π/2)] / (3π/4)
Simplifying further:
t = (2n + 1)(2/3)
The least positive value of t occurs when n = 0, because adding 1 to 2n will give us the smallest possible value. Therefore, for the least positive value of t, we substitute n = 0:
t = (2(0) + 1)(2/3) = 2/3
Hence, the least positive value of t for which d = 0 is t = 2/3.
To determine the least positive value of t for which d = 0, you need to solve the equation 0 = cos((3π/4)t).
The equation represents the cosine function with an argument of (3π/4)t. In order to find the value of t that satisfies the equation, you need to find the values of t that make the cosine of (3π/4)t equal to zero.
To do this, you need to find the values of (3π/4)t that correspond to the solutions of the equation cos((3π/4)t) = 0.
In general, the cosine function is equal to zero at the points where the argument is equal to an odd multiple of π/2. In other words, for any integer n, we have:
(3π/4)t = (2n + 1)(π/2)
To solve for t, you can divide both sides of the equation by 3π/4:
t = ((2n + 1)(π/2))/(3π/4)
Simplifying further, we can cancel out π and rearrange to get:
t = (8n + 4)/6
Now, you need to find the least positive value of t that satisfies the equation. Since n can be any integer, you want to find the smallest positive integer value of n that makes t positive.
To find the least positive value of t, consider setting n = 0:
t = (8(0) + 4)/6 = 4/6 = 2/3
Therefore, the least positive value of t for which d = 0 is t = 2/3.