Trigonometric Identities Worksheet With Answers Page 18
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2513-1 Trigonometric Identities
42. CCSS CRITIQUE Clyde and Rosalina are debating whether an equation from their homework assignment is an
identity. Clyde says that since he has tried ten specific values for the variable and all of them worked, it must be an
identity. Rosalina argues that specific values could only be used as counterexamples to prove that an equation is not
an identity. Is either of them correct? Explain your reasoning.
SOLUTION:
Rosalina; there may be other values for which the equation is not true.
43. CHALLENGE Find a counterexample to show that
is not an identity.
SOLUTION:
Sample answer: x = 45°
44. REASONING Demonstrate how the formula about illuminance from the beginning of the lesson can be rewritten to
show that
.
SOLUTION:
45. WRITING IN MATH Pythagoras is most famous for the Pythagorean Theorem. The identity
is
an example of a Pythagorean identity. Why do you think that this identity is classified in this way?
SOLUTION:
Sample answer: The functions
and
can be though of as the lengths of the legs of a right triangle, and the
number 1 can be thought of as the measure of the corresponding hypotenuse.
46. PROOF Prove that
by using the quotient and negative angle identities.
SOLUTION:
47. OPEN ENDED Write two expressions that are equivalent to
.
SOLUTION:
and
Sample answer:
48. REASONING Explain how you can use division to rewrite
as
.
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Page 18
SOLUTION:
Divide all of the terms by
.
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