Solve for t cos(t)=0

Problem

cos(t)=0

Solution

1. Identify the values on the unit circle where the cosine function equals zero. The cosine of an angle represents the xcoordinate of a point on the unit circle.

2. Determine the primary angles within one full rotation [0,2*π) where the xcoordinate is zero. These occur at the top and bottom of the circle.

θ=π/2

θ=(3*π)/2

3. Generalize the solution to include all possible rotations. Since the zeros of the cosine function occur every π radians, the solutions can be written using an integer n

t=π/2+n*π

Final Answer

cos(t)=0⇒t=π/2+n*π,n∈ℤ

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