Can you solve and show me the work in these two equations?
cos(3x)=-1
tan (theta)=-1
Best way to solve it is using a calculator and taking advantage of the arc functions (cos^-1 or tan^-1) to solve it.
arcCos^-1 (-1)= answer
arcTan^-1 (-1) = answer
if you can't use a calculator, then try to remember the unit circle.
cos(y) = -1 when y = pi or 180 degrees
So work backwards. cos y = cos 3x = -1
y=3x
x= pi/3 or 60 degrees. Since you didn't include bounds in the equation, the solution set is actually (60+120*n) where n is any integer. So x=60, 180, 300, 420... all work.
Same goes for the tangent. Just work backwards.
F&arrowbold;
Sure! Let's solve each equation step by step and show the work for each one.
1. Equation: cos(3x) = -1
To solve this equation, we need to find the values of x that satisfy the equation. First, we need to recall the values of cosine for different angles. The cosine function is equal to -1 when the angle is either 180 degrees or an odd multiple of 180 degrees (such as 540 degrees, 900 degrees, etc.). Therefore, we can write:
3x = 180 degrees + 360 degrees * n, where n is an integer.
Now, let's solve for x:
3x = 180 + 360n
x = (180 + 360n) / 3
x = 60 + 120n, where n is an integer.
Therefore, the solutions to the equation cos(3x) = -1 are x = 60 + 120n, where n is an integer. Each value of n corresponds to a different solution.
2. Equation: tan(theta) = -1
To solve this equation, we need to find the values of theta that satisfy the equation. The tangent function is equal to -1 when the angle is 135 degrees or an odd multiple of 135 degrees (such as 405 degrees, 675 degrees, etc.). Therefore, we can write:
theta = 135 degrees + 180 degrees * n, where n is an integer.
Now, let's solve for theta:
theta = 135 + 180n, where n is an integer.
Therefore, the solutions to the equation tan(theta) = -1 are theta = 135 + 180n, where n is an integer. Each value of n corresponds to a different solution.