Geometry Trig Lesson Test 2 Algebra 2 textbook, Prentice Hall, p.792

Objectives

Understand and use trigonometric relationships of acute angles in triangles.

Determine side lengths of right triangles by using trigonometric functions.

I can solve…

*Sin, Cos, Tan *Sin -1 , Cos -1 , Tan -1

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.

a

2 + b 2 = c 2

Pythagorean Theorem.

70 24

θ

Example 1 answers

Step 2 Find the function values.

• • •

SIX trigonometric function

sine cosine tangent • • • cosecants secant cotangent

Vocabulary

Example 2 Find the values of the six trigonometric functions for θ.

Step 1 Find the length of the hypotenuse.

a

2 + b 2 = c 2

Pythagorean Theorem.

80 18

θ

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.

a

2 + b 2 = c 2

Pythagorean Theorem.

70 24

θ

Example 3 answers

Step 2 Find the function values.

•

Application Assignment

Due next class; Copy on your own paper; in chart form (see below) B

TRI ID Ratio

sin A cos A tan A sin B cos B tan B

Inverse Trig ID

csc A

Ratio

Sec A cot A csc B cos B cot B C Info: AB = 25 CA = 16 CB = 9 A

I can solve for…

• Technology with trig functions

Clear calculators

Caution!

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.

first ALWAYS

• •

Steps:

2 nd  • +  • • 712  enter  • clear MODE  using arrow keys twice down and once over right  • enter  • • 2 nd  MODE.

Example 1

Use a calculator to find tan to the nearest ten thousandth.

KEYSTROKES

TAN ENTER

Answer:

Example 2: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.

sin 52 ° Caution!

Be sure your calculator is in degree mode, not radian mode.

sin 52 °  0.79

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) tan -1 (0.75)  35 ° cos -1 (0.05)  87 ° sin -1 (0.67)  42 °

I can solve… *Given degree and one side, solve for “ ? “

??

given

given

Step

one piece of paper

note taking skills

Example of step

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 What trig function contains OPPOSITE and HYPOTENUSE ?

sin = opp hyp

Fill in knowns and unknown, rearrange to solve for unknown

sin 30 = X 74

Example 1 cont. the term I am solving for is isolated, HEY!

74

sin 30 = X 74

74

Calculator: 74



sin



30



enter

X = 37

EX. 2 Use a trigonometric function to find the value of x.

Steps: Example of step: 1) What do I know ?

2) What trig function contains opposite and hypotenuse?

1) Hypotenuse & Opposite 2) Sine = opp hyp 3) Fill in knowns and unknowns 3) Sin 45 = X 4) Isolate what we are solving for 5) calculator 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 ??

***I can solve…

• Two degrees and one side give; solve for other side given ????

given