Geometry Trig Lesson Test 2 Algebra 2 textbook

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

Objectives Understand 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 actually six) trigonometric functions for θ. Step 1 Find the length of the hypotenuse. a 2 + b 2 = c 2 Pythagorean Theorem. 70 θ 24

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 θ 18

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 θ 24

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 Inverse Ratio Trig ID sin A csc A cos A Sec A tan A cot A sin B csc B cos B tan B cot B C A Info: AB = 25 CA = 16 CB = 9

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 KEYSTROKES: TAN Answer: 56 to the nearest ten thousandth. ENTER 1. 482560969

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° 0. 87

Example 4 Use your calculator to find each angle measure to the nearest degree. a. tan-1(0. 71) tan-1(0. 75) 35° b. cos-1(0. 05) 87° c. sin-1(0. 67) 42°

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

one piece of paper note taking skills Step Example of step

Ex. 1: Finding Side Lengths of Right Triangles Use a trigonometric function to find the value of x. E What trig function contains OPPOSITE and HYPOTENUSE ? T I S O opposite and hypotenuse P P O What do I know from image, what do I need ? H Y P O T E steps sin = opp hyp Fill in knowns and unknown, rearrange to solve for unknown sin 30 = X 74

Example 1 cont. he term I am solving 74 sin 30 = X 74 for is isolated, HEY! 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) Hypotenuse & Opposite 1) What do I know ? 2) Sine = opp 2) What trig function contains opposite and hypotenuse? hyp 3) Fill in knowns and unknowns 4) Isolate what we are solving for 5) calculator 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 • Given two sides, solve for degree (inverse? ? ) given ? ?

***I can solve… • Two degrees and one side give; solve for other side given ? ?