Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the following is equal to $\sin \left( \frac{\pi}{5} \right)$ ? $\newline$ A) $-\cos \left( \frac{\pi}{5} \right)$ $\newline$ B) $-\sin \left( \frac{\pi}{5} \right)$ $\newline$ C) $\cos \left( \frac{3\pi}{10} \right)$ $\newline$ D) $\sin\left( \frac{7\pi}{10} \right)$

View step-by-step help

View step-by-step help

Convert complex numbers between rectangular and polar form

Full solution

Q. Which of the following is equal to

\sin \left( \frac{\pi}{5} \right)

?

\newline

A)

-\cos \left( \frac{\pi}{5} \right)

\newline

B)

-\sin \left( \frac{\pi}{5} \right)

\newline

C)

\cos \left( \frac{3\pi}{10} \right)

\newline

D)

\sin\left( \frac{7\pi}{10} \right)

Understand Trigonometric Identities: Step $1$ : Understand the trigonometric identities. $\sin(\frac{\pi}{5})$ is a positive value since $\frac{\pi}{5}$ is in the first quadrant.
Evaluate Option A: Step $2$ : Evaluate option A. $\newline$ A) $−\cos(\frac{\pi}{5})$ - Since $\cos(\frac{\pi}{5})$ is positive in the first quadrant, $−\cos(\frac{\pi}{5})$ is negative. This cannot be equal to $\sin(\frac{\pi}{5})$ which is positive.
Evaluate Option B: Step $3$ : Evaluate option B. $\newline$ B) $-\sin(\frac{\pi}{5})$ - This is simply the negative of $\sin(\frac{\pi}{5})$ , which is positive. So, this option is also incorrect.
Evaluate Option C: Step $4$ : Evaluate option C. $\newline$ C) $\cos(\frac{3\pi}{10})$ - Using the identity $\cos(\theta) = \sin(\frac{\pi}{2} - \theta)$ , we get $\cos(\frac{3\pi}{10}) = \sin(\frac{\pi}{2} - \frac{3\pi}{10}) = \sin(\frac{\pi}{5})$ . This matches $\sin(\frac{\pi}{5})$ .
Evaluate Option D: Step $5$ : Evaluate option D. $\newline$ D) $\sin(\frac{7\pi}{10})$ - Using the identity $\sin(\pi - \theta) = \sin(\theta)$ , we get $\sin(\frac{7\pi}{10}) = \sin(\pi - \frac{7\pi}{10}) = \sin(\frac{3\pi}{10})$ . This is not equal to $\sin(\frac{\pi}{5})$ .

More problems from Convert complex numbers between rectangular and polar form

Question

Convert the equation to polar form. (Use variables

r

\theta

\newline

y=6x^{2}

Posted 2 months ago

Question

Convert the polar equation

\newline

r=\frac{5}{2\sin \theta-3\cos \theta}

to rectangular form.

Posted 2 months ago

Question

3\left[\cos \left(\frac{\pi}{2}\right)+i \sin \left(\frac{\pi}{2}\right)\right]

in rectangular form.

\newline

Simplify any radicals.

Posted 2 months ago

Question

Find the inverse

\newline

f(x)=\sqrt[3]{2x-7}

Posted 2 months ago

Question

2

1

1

\newline

\newline

\newline

Find the standard form of the equation of the hyperbola with the given characteristics.

\newline

( \pm 6,0)

( \pm 9,0)

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{6-6 i}{2-i}

\newline

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{22-24 i}{2-7 i}

\newline

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{-19-i}{10-9 i}

\newline

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{-9-6 i}{-5+2 i}

\newline

Posted 2 months ago

Question

Express as a complex number in simplest a+bi form:

\newline

\frac{4-22 i}{2+4 i}

\newline

Posted 2 months ago