Cc Geometry H Hw 26 Worksheet With Answers Page 3
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10Aim #27: What is the relationship between the sine and cosine
1-21-15
of complementary angles and special angles ?
Do Now: Given the diagram of the right triangle, complete the following table.
Calculate the hypotenuse in simplest radical form. Express all side lengths in
simplest radical form with rational denominators.
Angle Measure sin θ
cos θ
tan θ
s
s
2
t
4
t
a) Which values are equal?
b) How are tan t and tan s related?
How are the two co-functions (sine and cosine) related?
In right triangle ABC, the measurement of acute angle ≮ A is denoted
by α (alpha), and the measurement of acute angle ≮ B is denoted by β (beta).
α and β are a pair of _____________________ angles
B
Determine the following values in the table.
c
a
A
C
b
Based on the results in the above table, what can you conclude ?
• Since the ratios for sine α & cosine β are the same, ________ = ________.
• Since the ratios for cosine α & sine β are the same, ________ = ________ .
The sine of an angle is equal to the _______ of its ________________, and
the_________ of an angle is equal to the ___________ of its complement.
For complementary angles α and β, sin α = cos ____ and cos ___ = sin β.
Given measure θ such that 0 < θ < 90, cos (θ) = sin (90 - θ) and sin θ = cos (90 - θ).
Any two complementary angles can be the two ________ angles in a right triangle.
The co- prefix in cosine refers to the fact that the cosine of an angle
equals the sine of its ___________________.
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