geometry trig lesson test 2 algebra 2 textbook, prentice hall, p.792
TRANSCRIPT
Geometry Trig LessonTest 2
Algebra 2 textbook, Prentice Hall, p.792
Understand and use trigonometric relationships of acute angles in triangles.
Determine side lengths of right triangles by using trigonometric functions.
Objectives
*Sin, Cos, Tan
*Sin -1, Cos -1, Tan -1
I can solve…
Example 1: Finding Trigonometric Functions
Find the values of the three (there are actually six) trigonometric functions for θ.
Step 1 Find the length of the hypotenuse.
70
24
θ
a2 + b2 = c2 Pythagorean Theorem.
Example 1 answers
Step 2 Find the function values.
SIXtrigonometric function
• sine• cosine• tangent
• cosecants• secant• cotangent
Vocabulary
Find the values of the six trigonometric functions for θ.
Step 1 Find the length of the hypotenuse.
80
18
θ
a2 + b2 = c2 Pythagorean Theorem.
Example 2
Example 2 answers
Step 2 Find the function values.
Example 3: Finding All Trigonometric Functions
Find the values of the six trigonometric functions for θ.
Step 1 Find the length of the hypotenuse.
70
24
θ
a2 + b2 = c2 Pythagorean Theorem.
Example 3 answers
Step 2 Find the function values.
Application Assignment• Due next class; Copy on your own paper; in
chart form (see below)
TRI ID Ratio Inverse Trig ID
Ratio
sin A csc A
cos A Sec A
tan A cot A
sin B csc B
cos B cos B
tan B cot B
B
ACInfo:
AB = 25CA = 16CB = 9
I can solve for…
• Technology with trig functions
Make sure that your graphing calculator is set to interpret angle values as degrees. Press . Check that Degree and not Radian is highlighted in the third row.
Caution!
Clear calculators
first ALWAYS
Steps:• 2nd • +
• 712 • enter
• clear MODE • using arrow keys twice down and once over right
• enter • 2nd
• MODE.
Use a calculator to find tan to the nearest ten thousandth.
KEYSTROKES: 56 1.482560969TAN ENTER
Answer:
Example 1
Example 2: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
sin 52°
sin 52° 0.79
Be sure your calculator is in degree mode, not radian mode.
Caution!
Example 3
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
cos 30°
cos 30° 0.87
Example 4
Use your calculator to find each angle measure to the nearest degree.
a. tan-1(0.71) b. cos-1(0.05) c. sin-1(0.67)
cos-1(0.05) 87° sin-1(0.67) 42°tan-1(0.75) 35°
I can solve…
*Given degree and one side, solve for “ ? “
??
given
given
note taking skillsStep Example of step
one piece of paper
Ex. 1: Finding Side Lengths of Right Triangles
Use a trigonometric function to find the value of x.
steps
What do I know from image, what do I need ?
opposite and hypotenuse
OP
PO
SI
TE
H Y P O T E
What trig function contains OPPOSITE and HYPOTENUSE ?
sin = opp hyp
Fill in knowns and unknown, rearrange to solve for unknown
sin 30 = X 74
sin 30 = X 74
Example 1 cont.
7474the term I am solving for is
isolated, HEY!Calculator: 74 sin 30 enter
X = 37
EX. 2Use a trigonometric function to find the value of x.
Steps:
1) What do I know ?2) What trig function contains opposite and
hypotenuse?
3) Fill in knowns and unknowns
4) Isolate what we are solving for
5) calculator
Example of step:
1) Hypotenuse & Opposite
2) Sine = opp
hyp
3) Sin 45 = X
20
4) 20 sin 45
5) 14.14
Ex. 3
A surveyor whose eye level is 6 ft above the ground
measures the angle of elevation to the top of the highest
hill on a roller coaster to be 60.7°. If the surveyor is
standing 120 ft from the hill’s base, what is the height of
the hill to the nearest foot?
Ex. 4: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth. BC?
***I can solve…
• Given two sides, solve for degree (inverse????)
given
give
n
??
***I can solve…
• Two degrees and one side give; solve for other side
given
given
give
n
????