Question

Find the value of the trig function indicated.

Answer 1

Answer:

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

General Formulas and Concepts:

Pre-Algebra

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

Trigonometry

[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:

Step 1: Define

Identify variables

a = 8

b = 12

c

Step 2: Solve for c

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

Step 3: Define Pt. 2

Identify variables

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

Step 4: Find

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

Answer 2

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.