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Writing Trigonometric Equations From The Graph & Solving Word Problems

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You have seen quite a few trigonometric identities in the past few pages. It is convenient to have a summary of them for reference. These identities mostly refer to one angle denoted θ, but there are some that involve two angles, and for those, the two angles are denoted α and β.

The more important identities. You don't have to know all the identities off the top of your head. But these you should.

Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2 π while tangent and cotangent have period π.

The less important identities. You should know that there are these identities, but they are not as important as those mentioned above. They can all be derived from those above, but sometimes it takes a bit of work to do so.

The half angle formulas. The ones for sine and cosine take the positive or negative square root depending on the quadrant of the angle θ/2. For example, if θ/2 is an acute angle, then the positive root would be used.

Truly obscure identities. These are just here for perversity. No, not really. They have some applications, but they're usually narrow applications, and they could just as well be forgotten until needed.

Product identities. Aside: weirdly enough, these product identities were used before logarithms were invented in order to perform multiplication. Here's how you could use the second one. If you want to multiply x times y, use a table to look up the angle α whose cosine is x and the angle β whose cosine is y. Look up the cosines of the sum α + β. and the difference α - β. Average those two cosines. You get the product xy! Three table look-ups, and computing a sum, a difference, and an average rather than one multiplication. Tycho Brahe (1546-1601), among others, used this algorithm known as prosthaphaeresis.

More half-angle formulas. These describe the basic trig functions in terms of the tangent of half the angle. These are used in calculus for a particular kind of substitution in integrals sometimes called the Weierstrass t-substitution.

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You have seen quite a few trigonometric identities in the past few pages. It is convenient to have a summary of them for reference. These identities mostly refer to one angle denoted θ, but there are some that involve two angles, and for those, the two angles are denoted α and β.

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JMAP F.TF.C.9: Angle Sum and Difference Identities, Double and Half Angle Identities

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Math Bits Algebra 2 site will be helpful!

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Math Bits Algebra 2 site will be helpful!

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Trigonometric Graphs - MathBitsNotebook (Algebra2 - CCSS Math)

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Algebra 2 CCSS Lessons and Practice is a free site for students (and teachers) studying a second year of high school algebra.