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Trigonometric Values of Special Acute Angles with Examples | MMAT 3320, Study notes of Mathematics

University of Texas - Rio Grande ValleyMathematics
Prof. Roger A. Knobel

Material Type: Notes; Professor: Knobel; Class: Basics of Math Modeling; Subject: Middle School Mathematics; University: University of Texas - Pan American; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

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MMAT 3320 NOTES SECTION 9 PAGE 1
9 TRIGONOMETRIC VALUES OF SPECIAL ACUTE ANGLES
EXAMPLE 1. Consider the following isosceles right triangle.
x
45
°
45
°
a. Find the length of the remaining leg.
b. Find the length of the hypotenuse.
c. Find the value of cos 45°.
EXAMPLE 2. Consider the following 30°-60°-90° triangle.
30°
60°
a. Find the length of the hypotenuse.
b. Find the length of the remaining leg.
c. Find the value of sin 60°.
d. Find the value of tan 30°.
pf3
pf4
pf5

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9 TRIGONOMETRIC VALUES OF SPECIAL ACUTE ANGLES

EXAMPLE 1. Consider the following isosceles right triangle.

x

45 °

45 °

a. Find the length of the remaining leg.

b. Find the length of the hypotenuse.

c. Find the value of cos 45°.

EXAMPLE 2. Consider the following 30°-60°-90° triangle.

a. Find the length of the hypotenuse.

b. Find the length of the remaining leg.

c. Find the value of sin 60°.

d. Find the value of tan 30°.

EXAMPLE 3. Consider the following 15°-75°-90° triangle.

(^75) °

1 5°

Find the value of cos 15°.

HOMEWORK

  1. Find the (exact) value of each of the following. a. sin 45° b. cos 30° c. tan 60° d. sin 30° e. tan 45° f. cos 60°
  2. Consider the following 15°-75°-90° triangle.

(^75) °

1 5°

a. Find the (exact) value of sin 15°. b. Find the (exact) value of tan 15°. c. Find the (exact) value of cos 75°. d. Find the (exact) value of sin 75°. e. Find the (exact) value of tan 75°.

  1. Find the (exact) value of each of the following. a. cos^230 ° + sin^230 ° b. cos^245 ° + sin^245 ° c. cos^260 ° + sin^260 ° d. cos^215 ° + sin^215 ° e. cos^275 ° + sin^275 °
  2. Based on the results of the previous problem, make a conjecture.
  3. Based on earlier results, complete the following. a. cos 30° = sin _____ b. cos 45° = sin _____ c. cos 60° = sin _____ d. cos 15° = sin _____ e. cos 75° = sin _____
  4. Based on the results of the previous problem, a. make a conjecture.

b. Based on your conjecture, complete the following: cos 18° = sin _____ c. Use your calculator to verify your answer in part b.

  1. Based on earlier results, complete the following. a. sin 30° = cos _____ b. sin 45° = cos _____ c. sin 60° = cos _____ d. sin 15° = cos _____ e. sin 75° = cos _____
  2. Make a conjecture based on the results of the previous problem.

ANSWERS

1a.

1b.

1c. 3

1d.

1e. 1

1f.

2a.

2b. 2 - 3

2c. 6 2 4

2d.

2e. 2 + 3