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Yanka [14]
2 years ago
7

Find the value of the trig function indicated.

Mathematics
2 answers:
11Alexandr11 [23.1K]2 years ago
7 0

Answer:

Solution given;

In right angled triangle with respect to θ

perpendicular: opposite side: [P]=12

base:adjacent:[b]=8

hypotenuse [h]=?

cosθ=?

According to the Pythagoras law

h²=p²+b²

h²=12²+8²

h=\sqrt{208}

h=4\sqrt{13}

Now

we have

Cos θ=\frac{adjacent}{hypotenuse}

Cos θ=\frac{8}{4\sqrt{13}}

by rationalising it

Cos θ= \frac{2\sqrt{13}}{\sqrt{13}×\sqrt{13}}

Cos θ= \frac{2\sqrt{13}}{13}

is a required answer.

jekas [21]2 years ago
6 0

Answer:

\displaystyle cos\theta = \frac{2\sqrt{13}}{13}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

  • a is a leg
  • b is another leg
  • c is the hypotenuse

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>a</em> = 8

<em>b</em> = 12

<em>c</em>

<u>Step 2: Solve for </u><em><u>c</u></em>

  1. Substitute in variables [Pythagorean Theorem]:                                          8² + 12² = c²
  2. Evaluate exponents:                                                                                       64 + 144 = c²
  3. Add:                                                                                                                 208 = c²
  4. [Equality Property] Square root both sides:                                                  √208 = c
  5. Rewrite:                                                                                                           c = √208
  6. Simplify:                                                                                                           c = 4√13

<u>Step 3: Define Pt. 2</u>

<em>Identify variables</em>

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

<u>Step 4: Find</u>

  1. Substitute in variables [Cosine]:                                                                   \displaystyle cos\theta = \frac{8}{4\sqrt{13}}
  2. Rationalize:                                                                                                     \displaystyle cos\theta = \frac{2\sqrt{13}}{13}
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