Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)

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Lesson Plan #80
Date: Monday April 19th, 2017
Class: Geometry
Topic: Cofunction relationships.
Aim: How can we use cofunction relationships?
Objectives:
1) Students will be able to use cofunction relationships.
HW # 80:
1) Write the expression as a function of an acute angle whose measure is less than 45 o.
A) sin 80o
B) sin 50o
C) cos 67o
D) cos 75o
2) Find the value of 𝜃
A) 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠10o
B) 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠𝜃
C) 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠2𝜃
D) 𝑠𝑖𝑛2𝜃 = cos⁡(𝜃 + 15)
Do Now:
1)
2)
3)
4)
5)
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Assignment #1:
The
reciprocal
of the
cosine ratio is the secant ratio, abbreviated sec.
What
is the sine
ratio?
Consider the reciprocal ratio of the sine ratio, namely hypotenuse over opposite.
This ratio is given a name, namely cosecant, abbreviated csc.
The reciprocal of the cosine ratio is secant, abbreviated sec.
The reciprocal of the tangent ratio is cotangent, abbreviated cot.
Examples:
In the triangle at right, find
A) sin A
B) cos A ________
C) tan A ________
D) sin B ______ E) cos B ________
F) tan B ________
G) sec A ______ H) sec B _______
I) csc A ______ J) csc B _______
K) cot A ______ L) cot B _______
Find sin60o.
Find cos 30o.
What relationship exists between the angles above?
Using your calculator,
find sin 20o
find cos 70o
What relationship exists between these angles?
Sin and cosine are cofunctions. What are other pairs of cofunctions? _______________________________________
Find sec 30o. _________
Find csc 60o. _________
Find tan 30o
Find cot 60o
What can we say about the trig function of an acute angle and the cofunction of its complement?
Examples: Find x, given that the equations below refer to trigonometric functions of acute angles.
A) sin x = cos(2x + 45)
B) sin(x+20)= cosx
C) cot(x +10) = tan3x
Past Regents Questions:
1)
D) sec(x + 12) = csc (x + 8)
2
3
2)
3)
4) In ABC , where C is a right angle,
cos A 
5) Find the value of R that will make the equation
6)
7)
8)
21
, what is sin B ?
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sin 73o  cos R true when 0o  R  90o .
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If enough time:
1)
2) In the diagram below, a window of a house is 15 feet above the ground. A ladder is placed against
the house with its base at an angle of 75o with the ground. Determine and state the length of the
ladder to the nearest tenth of a foot.
3) If
√13
, and 𝑠𝑒𝑐𝜃 =
, find
0o    90o and 𝑐𝑠𝑐𝜃 = √13
2
3
4) Find sec 4o50’15”
If enough time, Pythagorean identities.
A) sin 𝜃
C) tan 𝜃
B) cos 𝜃
D) sec (90 – 𝜃)