Download 9-7 cofunctions

Name______________________________________
Geometry Period_____
9-7 Notes
Date_________
Lesson 9-7: Re-writing Trigonometric Expressions-Cofunctions
Today’s Aim: How can we use relationships within right triangles to help us re-write Trigonometric ratios?
Let’s Re-activate our knowledge
What do we call these different parts of a trig function?
The _____________ (
function.
) of the trig
The ______________ or ______________
of the trig function.
Often, mathematicians will use Greek letters to identify an angle in a
right triangle.
Theta
Try writing some here:
______
Gamma
Try writing some here: _______________
Group Exploration
READ and answer the following questions in your groups:
1. What type of triangle is shown here? How do you know?
2. Using your answer from Question # 1 and your knowledge of the interior
angles of triangles, what MUST be the sum of 𝜃 𝑎𝑛𝑑 𝛾 ?
Therefore the two non-right angles in a right triangle must always be
3. Write the indicated trig ratios using the sides of the triangle shown above :
𝐶𝑜𝑠 𝜃=
𝑆𝑖𝑛 𝛾 =
4. What do you notice about these values?
a) Will this be true for ALL right triangles? Try another ( Triangle ABC)
𝐶𝑜𝑠 𝑥 =
𝑆𝑖𝑛 𝑦 =
.
Let’s summarize as a class:
The VALUE of sine of an acute angle is equal to the _
complement.
Symbols:
of its
Example:
The VALUE of cosine of an acute angle is equal to the
complement.
Symbols:
of its
Example:
We call Sine and Cosine
.
Let’s try!
1. Write each expression as a function of an acute angle.
a.
sin 80˚
b. cos 36˚
2. Each equation contains the measures of two acute angles. Find a value of θ for which the statement is true.
Remember!
In cofunctions, VALUES are equal and ANGLES are
complements.
1) sin 10° = cos θ
2) sin θ = cos 2θ
3. In right triangle ABC with the right angle at C, sin A = 2x + 0.1 and cos B = 4x – 0.7.
Determine and state the value of x. Explain your answer.
You’re Turn!
4) Write the expression in terms of sine and/or cosine.
A) sin 7
B) cos 31
5) Which ratios are equal to ½? Select all that apply:
a. sinL
b. cosL
c. sinJ
d. cosJ
6) Write sin(30°) in terms of its co-function.
𝑥
𝑥
7) Math-Hoo uses the equation sin49 = 16 to find BC. His cousin Hal uses the equation cos41 = 16 to find BC. Who is
correct? Explain.
Fill it in!
8)
7) In
, the complement of
is
. Which statement is always true?
1)
2)
3)
4)
8) In right triangle ABC with the right angle at C, sin A = 2x + 5 and cos B = 4x – 15. Solve for x.
Explain your solution.
Name_____________________________________
Geometry Period______
9-7 HW
Date_________
1) Find sin J, sin K, cos J, and cos K. Write each answer as a ratio.
2) Write the expression in terms of sine or cosine.
a) sin 22 = cos ________
b) cos 56
c) cos 15
3) Find the value of x and y. Round to the nearest tenth.
4) The angle of depression is 11 from the bottom of a boat to a deep sea diver at a depth of 120 feet. Find the distance
x the diver must swim up to the boat to the nearest foot.
5) In
, where
is a right angle,
6) Find the value of R that will make the equation
. What is
?
true when
. Explain your answer.
7) In right triangle ABC with the right angle at C, sin A = 3x + 5 and cos B = x –40. Solve for x.