How do the graphs of sine and cosine relate to each of the others? a) Tangent?
Tangent's ratio identity is sin/cos. As cosine equals zero, tan is undefined meaning it will not touch wherever cosine equals zero. As sine equals zero however, tan will intersect the x-axis because tan will equal zero.
Cotangent's ratio identity is cos/sin. As sine equals zero, cot is undefined meaning it will not touch wherever sine equals zero. As cosine equals zero however, cot will intersect the x-axis because cot will equal zero.
Secant's reciprocal identity is 1/cos. That means whenever cosine equals 0, then secant will be undefined and will never touch wherever cosine equals 0. When cosine equals 1, secant will equal 1 thus the amplitudes of secant and cosine will touch.
Cosecant's reciprocal identity is 1/sin. That means whenever sine equals 0, cosecant will be undefined and will never touch wherever sine equals 0. When sine equals 1, cosecant will equal 1 thus the amplitudes of cosecant and sine will touch.