All categories

3 years ago

Solve for x on the interval [0, 2pi] Sinx = cosx + 1

Mathematics

1 answer:

lisov135 [29]3 years ago

8 0

Answer:

Step-by-step explanation:

Solve for x on the interval [0, 2pi]

Given the equation

Sinx = cosx + 1

Square both sides of the equation

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms

1-1-cos²x-cos²x-2cos x = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = arccos -1

x = 180 degrees

Hence the value of x = π

You might be interested in

Solve the equation using square roots. Write your answer in simplest form. Question in picture

GalinKa [24]

Answer:

The solutions to the quadratic equation involving square roots are:

$x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8$

Step-by-step explanation:

Given the equation

$\frac{1}{4}\left(x-8\right)^2+8=1$

subtract 8 from both sides

$\frac{1}{4}\left(x-8\right)^2+8-8=1-8$

$\frac{1}{4}\left(x-8\right)^2=-7$

$\left(x-8\right)^2=-28$

$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

solving

$x-8=\sqrt{-28}$

$x-8=\sqrt{-1}\sqrt{28}$

$x-8=\sqrt{28}i$ ∵ $\sqrt{-1}=i$

$x=2\sqrt{7}i+8$

similarly solving

$x-8=-\sqrt{-28}$

$x-8=-2\sqrt{7}i$

$x=-2\sqrt{7}i+8$

Therefore, the solutions to the quadratic equation involving square roots are:

$x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8$

5 0

3 years ago

In the diagram AB is parallel to CD. What is the term for the line that intersects the two parallel lines?

icang [17]

A transversal line is the term for a line that intersects two parallel lines.

4 0

3 years ago

Read 2 more answers

What's the GCF of 30,48,60

scoray [572]

The greatest common factor (GCF) of 30, 48, and 60 is: 6

Factors for 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

The common factors between them are 1, 2, 3, and 6, but 6 is the greatest.

6 0

3 years ago

What is the quotient of -8a^8b^-2/ 10a^-4b^-10 in simplified form?

postnew [5]

Here are a few rules with exponents that you need to know: