Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find all solutions with $- \frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$ . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas. $\csc(\theta)=1$

View step-by-step help

View step-by-step help

Solve trigonometric equations

Full solution

Q. Find all solutions with

- \frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\csc(\theta)=1

Understand $csc(\theta):$ Step $1$ : Understand the function $csc(\theta)$ and its relation to $\sin(\theta)$ . $csc(\theta) = \frac{1}{\sin(\theta)}$ . We need to find $\theta$ such that $csc(\theta) = 1$ , which implies $\sin(\theta) = 1$ .
Find $\theta$ for $\csc(\theta) = 1$ : Step $2$ : Recall the values of $\theta$ where $\sin(\theta) = 1$ within the interval $-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$ . The only angle where $\sin(\theta) = 1$ in this interval is $\theta = \frac{\pi}{2}$ .

More problems from Solve trigonometric equations

Question

Marco's class is painting a mural on the side of their school. The mural covers a

3 \frac{1}{2} \mathrm{~m}

high, rectangular wall. It has an area of

28 \mathrm{~m}^{2}

\newline

What is the length of the mural?

\newline

Posted 3 months ago

Question

A cup of hot coffee has been left to cool in a room with an ambient temperature of

21^{\circ} \mathrm{C}

\newline

The relationship between the elapsed time,

m

, in minutes, since the coffee was left to cool, and the temperature of the coffee,

T

{ }^{\circ} \mathrm{C}

, is modeled by the following function.

\newline

T(m)=21+74 \cdot 10^{-0.03 m}

\newline

What will the temperature of the coffee be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

{ }^{\circ} C

Posted 3 months ago

Question

Takumi plants a tree in his backyard and studies how the number of branches grows over time.

\newline

He predicts that the relationship between

N

, the number of branches on the tree, and

t

, the elapsed time, in years, since the tree was planted can be modeled by the following equation.

\newline

N=5 \cdot 10^{0.3 t}

\newline

According to Takumi's model, in how many years will the tree have

100

\newline

Give an exact answer expressed as a base

-10

\newline

Posted 3 months ago

Question

g(x)=2^{x}

\newline

Can we use the mean value theorem to say the equation

g^{\prime}(x)=16

has a solution where

3<x<5

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

g

over the interval

3 \leq x \leq 5

1 \overline{6}

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

Posted 3 months ago

Question

\frac{d}{d x}\left(\frac{x^{2}-x+5}{4 x-1}\right)=

Posted 3 months ago

Question

\frac{d}{d x}\left(\frac{2 x^{2}+x-3}{2 x+7}\right)=

Posted 3 months ago

Question

\frac{d}{d x}\left(\frac{3 x^{2}-1}{x-2}\right)=

Posted 3 months ago

Question

\frac{d y}{d t}=2 t+3 \text { and } y(1)=6

\newline

t

y=0

\newline

Choose all answers that apply:

\newline

t=-1

\newline

t=-3

\newline

t=0

\newline

t=-4

\newline

t=1

\newline

t=-2

Posted 3 months ago

Question

\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=

Posted 3 months ago

Question

y=x^{13}

\newline

\frac{d y}{d x}=

Posted 3 months ago