Warm-UpWarm-Up

Pg. 454

#56, 58

Warm-UpWarm-Up pg. 454pg. 454

5 (3) = x

15 = x

Warm-UpWarm-Up pg. 454pg. 454

0.5 k = 10

k = 10 / 0.5

k = 20

Homework QuestionsHomework Questions

Homework Answers

Homework Answers

Homework Answers

Homework Answers

Homework Answers

Homework Answers

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Homework Worksheet: DAILY GRADE!!!

Lesson 8-4 Lesson 8-4 TrigonometryTrigonometry

pp. 456-462

ObjectivesObjectives

• Find trigonometric ratios using right triangles.• Solve problems using trigonometric ratios.

BenchmarksBenchmarks

• 1b. Given exact irrational solutions, determine the best rational estimation. (DOK 2)

• 1c. Solve real-world or application problems that involve square roots and the Pythagorean Theorem. (DOK 3)

• 4b. Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions. (DOK 2)

• 4e. Apply the relationships of sine, cosine, and tangent to problems involving right triangles. (DOK 2)

SineSine

Sin Sin A = A = leg opposite of leg opposite of AA hypotenusehypotenuse

hypotenuse

hypotenuse leg leg opposite opposite

of of AA

CosineCosine

Cos Cos A = A = leg adjacent to leg adjacent to AA hypotenusehypotenuse

hypotenuse

hypotenuse

leg adjacent to leg adjacent to AA

TangentTangent

Tan Tan A = A = leg opposite leg opposite AA leg adjacent leg adjacent AA

leg opposite leg opposite AA

leg adjacent to leg adjacent to AA

Memory Hint #1Memory Hint #1

SIN: OPPOSITE OVER HYPOTENUSE

COS: ADJACENT OVER HYPOTENUSE

TAN: OPPOSITE OVER ADJACENT

Memory Hint #2Memory Hint #2

SIN: OPPOSITEOPPOSITE OVER HYPOTENUSEHYPOTENUSE

COS: ADJACENTADJACENT OVER HYPOTENUSEHYPOTENUSE

TAN: OPPOSITEOPPOSITE OVER ADJACENTADJACENT

SSome OOld HHag CCracked AAll HHer TTeeth OOn AApples

Check Your ProgressCheck Your Progress p. 456p. 456

1. Find sin J, cos J, tan J, sin K, cos K, and tan K. Express each ratio as a fraction and as a decimal.

131355

1212

First, First, label thelabel the

sidessides.

For angle J,For angle J,label the label the O, A, & H.O, A, & H.

Now, Now, for angle K,for angle K,

label the label the O, A, & H.O, A, & H.

Check Your ProgressCheck Your Progress p. 456p. 456

sin J =

cos J =

tan J =

sin K =

cos K =

tan K =

131355

1212

5 / 13

Fraction & Decimal

= 0.3846

12 / 13 = 0.9231

5 / 12 = 0.4167

Fraction & Decimal

12 / 13 = 0.9231

5 / 13 = 0.3846

12 / 5 = 2.4

NoteNote

You can use the calculator to find the trigonometric ratios.

Be sure your calculator is in degree mode.

Press the DRGDRG button to swap between the different modes. The screen should read DEG.

Check Your ProgressCheck Your Progress p. 458p. 458

2. Sin 67 =

0.9205

In the calculator,In the calculator,Type 67Type 67

Press the “SIN” button.Press the “SIN” button.

Check Your UnderstandingCheck Your Understanding p. 460p. 460

3. Sin 57 = 0.8387

4. Cos 60 = 0.5

5. Cos 33 = 0.8387

6. Tan 30 = 0.5774

7. Tan 45 = 1

8. Sin 85 = 0.9962

QuestionsQuestions

AssignmentAssignment

PracticePractice

p. 460 p. 460

#14 – 23#14 – 23

Extra PracticeExtra Practice

GeometryOnline.comGeometryOnline.com

Self-Check QuizSelf-Check QuizLesson 8-4Lesson 8-4