Graphs of the Inverse Trig FunctionsWhen we studied inverse functions in general (see Inverse Functions), we learned that the inverse of a function can be formed by reflecting the graph over the identity line y = x. We also learned that the inverse of a…

The Graphs of y = tan(x), y = sec(x), y = csc(x), y = cot(x)Graphs of trigonometric functions can be produced in degrees or in radians. The graphs appearing here will be done in radians.Hint: When hand-drawing the graphs of sine and cosine, draw vertica…

Deriving Law of Sines and Law of CosinesOur friend, the Pythagorean Theorem, comes to our aid when solving for sides and/or angles in a right triangle. We have now seen that there are formulas (the Law of Sines and the Law of Cosines) that will help us f…

Pythagorean IdentitiesWhen studying the unit circle, it was observed that a point on the unit circle (the vertex of the right triangle) can be represented by the coordinates  (cos θ, sinθ)Since the legs of the right triangle in the unit circle have the …

Ambiguous Case Law of SinesIn Geometry, we found that we could prove two triangles congruent using:SAS – Side, Angle, Side ASA – Angle, Side, Angle AAS – Angle, Angle, Side SSS – Side, Side, Side HL – Hypotenuse Leg for Right Triangles. We also discover…

The Important Angles Be sure you know, or know how to quickly determine, the following information. If you know the special right triangles and the trig graphs you already know how to determine this information.

Vocabulary for Working with Trigonometric GraphsA sine wave, or sinusoid, is the graph of the sine function in trigonometry. In addition to mathematics, this function also occurs in other fields of study such as science and engineering. This wave pattern…

Horizontal Shift – Phase Shifthorizontal shift and phase shift: If the horizontal shift is positive, the shifting moves to the right. If the horizontal shift is negative, the shifting moves to the left. From the sinusoidal equation,y = A sin (B(x-C)) + …

Review of TransformationsLet’s start with a review of transformations in the coordinate plane.Line Reflections Remember that a reflection is simply a flip. Under a reflection, the figure does not change size (it is an isometry). It is simply flipped ove…

Unit Circle and Trig Value SignsA unit circle is a circle with a radius of one (a unit radius). In trigonometry, the unit circle is centered at the origin.For the point (x,y) in Quadrant I, the lengths x and y become the legs of a right triangle whose h…