Transcript Geometry_8-4 Trigonometry_2014-Day2
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
Homework Answers
Homework Answers
Homework Answers
Homework Answers
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