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

????