By Sarah Drake Brown
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Additional resources for A Teacher's Guide to The Bill of Rights: A History in Documents
E. angles that are the sum or the difference of two other angles) can be expressed in terms of trig functions of the single angles. For example, sin of (A + B) can be expressed as a combination of the sum and products of the sin and cos of A and B separately. Similarly, since we know that sin(−A) = − sin A, and cos(−A) = cos A, we can derive sin(A − B). By judicious substitution (using B = A), sin(A + B) can be changed to sin 2A and then into sin A (using A = 2(A/2)). In earlier days, before calculators and computers were available, knowledge of the trig functions of compound angles was invaluable in practical workplace calculations.
H +ve hypotenuse always has a positive value. e. between 0◦ and 180◦ ) are always positive as seen in the graph on the opposite page, rising from 0 for sin 0 ◦ to a maximum value of 1 for sin 90◦ . e. between 180◦ and 360◦ ) are all negative, going to a minimum of −1 for sin 270◦ , and returning to 0 for sine 360◦ . The brain remembers pictures better than equations or words; so commit the graph on the opposite page to memory; and this would prove to be extremely valuable in solving trig problems.
G. 123 000 means that the LHS has 1 sin, 2 cos, 3 tan and no cosec, sec and cot functions. On the rare occasion when you cannot find the identity in the Concordance, use the functions on the RHS to determine the code.