Can someone please help find X.

Mathematics

1 answer:

Vera_Pavlovna [14]4 years ago

4 0

Answer:

32°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the trig function relating angles to the opposite and adjacent sides of the triangle is ...

Tan = Opposite/Adjacent

The side opposite the angle x is shown as having measure 5; the side adjacent has measure 8. Putting all this in the above equation gives ...

tan(x) = 5/8

To find the angle from the value of the tangent, you use the inverse of the tangent function. The name of that is the arctangent function. It is often written as tan⁻¹(x) and often accessible on your calculator using a "second function" key. Some calculators, like the one shown in the attachment, recognize the arctan function name.

x = arctan(5/8) ≈ 32°

The value of x rounded to the nearest whole degree is 32°.

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What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

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Answer:

B) 4√2

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

Integrals
Definite Integrals
Integration Constant C

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$