Write three trigonometric equations each with the complete solution
pi+2pin
cosθ+1 = 0
cot(θ/2) = 0
Thank you
To find three trigonometric equations with the complete solution of pi + 2pi*n, where n is an integer, we can consider the sine (sin), cosine (cos), and tangent (tan) functions. The complete solution means that all values of x that satisfy the equation are included.
1. Sine equation: sin(x) = sin(pi + 2pi*n)
The sine function has a periodicity of 2pi, meaning that sin(pi + 2pi*n) is equal to sin(pi) for all integer values of n. So, the complete solution is x = pi.
2. Cosine equation: cos(x) = cos(pi + 2pi*n)
Similar to the sine function, the cosine function is also periodic with a period of 2pi. Thus, cos(pi + 2pi*n) is equal to cos(pi) for all integer values of n. Therefore, the complete solution is x = pi.
3. Tangent equation: tan(x) = tan(pi + 2pi*n)
The tangent function has a periodicity of pi, so tan(pi + 2pi*n) is equal to tan(0) for all integer values of n. Hence, the complete solution is x = 0.
Therefore, the three trigonometric equations with the complete solution of pi + 2pi*n are:
1. sin(x) = sin(pi)
2. cos(x) = cos(pi)
3. tan(x) = tan(0)