Mathematics, 27.05.2021 23:00 carrieaj08

Find the value of the trig function indicated.

Answers: 3

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Answer from: tylorroundy

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Trigonometry

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

a is a legb is another legc 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

Step 2: Solve for c

Substitute in variables [Pythagorean Theorem]: 8² + 12² = c²Evaluate exponents: 64 + 144 = c²Add: 208 = c²[Equality Property] Square root both sides: √208 = cRewrite: c = √208Simplify: c = 4√13

Step 3: Define Pt. 2

Identify variables

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

Step 4: Find

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

Answer from: bryan9892

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.

Answer from: Quest

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did not satisfy the given simplify expression.

Answer from: Quest

step-by-step explanation:

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