45 – Rewriting Trigonometric Expressions No Calculator Trigonometric Investigations II 45 – Rewriting Trigonometric Expressions No Calculator

Since final answer has cos x only, rewrite sin x in terms of cos x Not all trigonometric expressions can be rewritten as a single trig function or constant.

Since final answer has cos x only, rewrite tan x in terms of sin x and cos x

Since final answer has only one term, combine the two terms into one (common denominator)

Since final answer has only one term, combine the two terms into one (common denominator)

Since final answer has only one term, combine the two terms into one in both numerator and denominator (common denominator) Divide fractions…multiply by reciprocal Need common den in denominator

OPTION 1 Since final answer has only one term, combine the two terms into one (common denominator) –1

OPTION 2 Since final answer has only cos x, eliminate sin x Both options 1 and 2 are correct, and would receive full credit. There is more than one solution to MANY problems.

Need cot x in the numerator…can do that via Pythagorean identity. Intentionally did NOT multiply denominator (see answer)

Answer is a fraction…rewrite as a fraction. Need cos x in the denominator

Want tangent in the numerator… Multiply by “1”

What do I multiply the denominator by to get the denominator in the answer? Whatever it is, do the same in the numerator and see what happens.

One fraction given…two terms in the answer…separate…

Two terms in the problem…combined into one term. (common denominator)