Question

evaluate cos 2 pi by 17 using equation x to the power 17 - 1 is equal to zero​

Answer 1

Answer:

Practice set 1: Basic equations

Example: Solving \sin(x)=0.55sin(x)=0.55sine, left parenthesis, x, right parenthesis, equals, 0, point, 55

Let's use the calculator and round to the nearest hundredth.

\sin^{-1}(0.55)=0.58sin−1(0.55)=0.58sine, start superscript, minus, 1, end superscript, left parenthesis, 0, point, 55, right parenthesis, equals, 0, point, 58

(We are using radians.)

We can use the identity \sin(\pi-\theta)=\sin(\theta)sin(π−θ)=sin(θ)sine, left parenthesis, pi, minus, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis to find the second solution within [0,2\pi][0,2π]open bracket, 0, comma, 2, pi, close bracket.

\pi-0.58=2.56π−0.58=2.56pi, minus, 0, point, 58, equals, 2, point, 56

We use the identity \sin(\theta+2\pi)=\sin(\theta)sin(θ+2π)=sin(θ)sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis to extend the two solutions we found to all solutions.

x=0.58+n\cdot2\pix=0.58+n⋅2πx, equals, 0, point, 58, plus, n, dot, 2, pi

x=2.56+n\cdot2\pix=2.56+n⋅2πx, equals, 2, point, 56, plus, n, dot, 2, pi

Here, nnn is any integer.

Check your understanding

PROBLEM 1.1

Select one or more expressions that together represent all solutions to the equation.

The answers are in radians. nnn is any integer.

\cos(x)=0.15cos(x)=0.15cosine, left parenthesis, x, right parenthesis, equals, 0, point, 15

Choose all answers that apply:

Choose all answers that apply:

(Choice A)

A

-2.99+n\cdot\pi−2.99+n⋅πminus, 2, point, 99, plus, n, dot, pi

(Choice B)

B

-1.42+n\cdot2\pi−1.42+n⋅2πminus, 1, point, 42, plus, n, dot, 2, pi

(Choice C)

C

1.42+n\cdot\pi1.42+n⋅π1, point, 42, plus, n, dot, pi

(Choice D)

D

1.42+n\cdot2\pi1.42+n⋅2π1, point, 42, plus, n, dot, 2, pi

(Choice E)

E

4.56+n\cdot\pi4.56+n⋅π4, point, 56, plus, n, dot, pi