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The 6 Trigonometric Functions Solutions

• Trigonometry studies the relationship between angles and side lengths of triangles.
• Trigonometric functions cycle through the same values over and over in a repeating pattern (as compared to the other families of functions in this course: polynomials, radicals, logarithmic, etc.)
• There are six foundational trigonometry functions:
  • sine (sin)
  • tangent (tan)
  • secant (sec)
  • cosine (cos)
  • cotangent (cot)
  • cosecant (csc)
• Each trigonometric function is periodic, meaning each repeats its values at regular intervals across the x-axis.
• Sine, cosine, secant, and cosecant repeat values across an interval of $2\mathrm{\pi }$.
• Tangent and cotangent repeat values across an interval of $\mathrm{\pi }$.

• For the parent graphs of the trigonometric functions, the scale of the x-axis is adjusted.
• For sine, cosine, secant, and cosecant, the scale of the x-axis increases or decreases by  $\frac{\mathrm{\pi }}{2}$.
• For tangent and cotangent, the scale of the x-axis increases or decreases by $\frac{\mathrm{\pi }}{4}$.
• The scale of the y-axis increases or decreases by one.
• Each trigonometric function includes five key elements on the graph, which consist of intercepts and asymptotes.