Warm-Up Pg. 454 #56, 58

Warm-Up pg. 454 5 (3) = x 15 = x

Warm-Up pg. 454 0.5 k = 10 k = 10 / 0.5 k = 20

Homework Questions

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Homework Answers

Homework Answers

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Homework Answers

Homework Answers

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Lesson 8-4 Trigonometry

pp. 456-462

Objectives

• • Find trigonometric ratios using right triangles.

Solve problems using trigonometric ratios.

Benchmarks

• • • • 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)

Sine

Sin



A = leg opposite of



A hypotenuse leg opposite of



A

Cosine

leg adjacent to



A Cos



A = leg adjacent to



A hypotenuse

Tangent

leg adjacent to



A Tan



A = leg opposite



A leg adjacent



A leg opposite



A

Memory Hint #1

SIN: OPPOSITE OVER HYPOTENUSE COS: ADJACENT OVER HYPOTENUSE TAN: OPPOSITE OVER ADJACENT

Memory Hint #2 S

ome

O

ld

H

ag

C

racked

A

ll

H

er

T

eeth

O

n

A

pples

SIN:

OPPOSITE OVER HYPOTENUSE

COS:

ADJACENT OVER HYPOTENUSE

TAN:

OPPOSITE OVER ADJACENT

Check Your Progress p. 456 5 12

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.

First, label the sides

.

Check Your Progress p. 456 Now, For angle J, for angle K, label the label the O, A, & H.

O, A, & H.

5

Fraction & Decimal sin J =

5 / 13 = 0.3846

cos J =

12 / 13 = 0.9231

tan J =

5 / 12 = 0.4167

sin K =

12

Fraction & Decimal

12 / 13 = 0.9231

cos K =

5 / 13 = 0.3846

tan K =

12 / 5 = 2.4

Note

You can use the calculator to find the trigonometric ratios.

Be sure your calculator is in degree mode. Press the DRG button to swap between the different modes. The screen should read DEG.

Check Your Progress p. 458

2. Sin 67  =

0.9205

In the calculator, Type 67 Press the “SIN” button.

Check Your Understanding

3. Sin 57  = 4. Cos 60  = 5. Cos 33  = 6. Tan 30  = 7. Tan 45  = 8. Sin 85  = 0.8387 0.5

0.8387

0.5774

1 0.9962

p. 460

Questions

Practice Assignment Extra Practice p. 460 #14 – 23 GeometryOnline.com

Self-Check Quiz Lesson 8-4