A reduction formula is one that can be used to "reduce" the number of terms in the input for a trigonometric function. Explain how the figure shows that the following reduction formulas are valid. sin(t + 7) = -sin(t) cos(t + T) = -cos(t) tan(t + n) = tan(t) (x, y) 1 (-x, –y)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 59E
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A reduction formula is one that can be used to "reduce" the number of terms in the input for a trigonometric function. Explain how the figure shows that the following reduction formulas are valid.
sin(t + t) = -sin(t) cos(t + Tt) = -cos(t)
tan(t + n) = tan(t)
YA
t + ™
(x, y)
1
(-x,-y)
Notice that if P(t) = (x, y), then P(t + t) = (-x, -y). Thus,
sin(t + 1) =
-sin(t)
and sin(t) =
-sin(t+a)
Therefore, sin(t + 1) = -sin(t).
-cos(t)
and cos(t) =
|-cos (1+ 1)
· Therefore, cos(t + t) = -cos(t).
cos(t + T) =
sin(t)
-sin(1)
sin(t)
sin(t + t)
cos(t + 1)
tan(t + 1) =
= tan(t).
cos(1)
Transcribed Image Text:A reduction formula is one that can be used to "reduce" the number of terms in the input for a trigonometric function. Explain how the figure shows that the following reduction formulas are valid. sin(t + t) = -sin(t) cos(t + Tt) = -cos(t) tan(t + n) = tan(t) YA t + ™ (x, y) 1 (-x,-y) Notice that if P(t) = (x, y), then P(t + t) = (-x, -y). Thus, sin(t + 1) = -sin(t) and sin(t) = -sin(t+a) Therefore, sin(t + 1) = -sin(t). -cos(t) and cos(t) = |-cos (1+ 1) · Therefore, cos(t + t) = -cos(t). cos(t + T) = sin(t) -sin(1) sin(t) sin(t + t) cos(t + 1) tan(t + 1) = = tan(t). cos(1)
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