#### Values of inverse trigonometric functions

Compute the value of $x$ that satifies the equation $6\arcsin\left(x+7\right)-4\;\text{arccot}(-1)=0$

# Functions of one variable

Training
13

#### Graphs - Inverse trigonometric functions

Consider the following functions: $f_1(x)=\arccos\left(-\frac{x}{4}\right)-\frac{\pi}{4}$ $f_2(x)=\frac{\pi}{4}+\arctan(2x)$ $f_3(x)=\frac{\pi}{4}-\arcsin\left(\frac{x}{4}\right)$ $f_4(x)=\text{arccotan}(2x)-\frac{\pi}{4}$ Match each function with its respective graph shown in the figure.

# Functions of one variable

Reasoning
13

#### Chain rule arcsin

Let $f$ be a diferentiable function in $\mathbb{R}$ and $g(x)=f(\pi/2+\arcsin(2x-1))$. Find the derivative of $g$ at the point where the line $2x-2y=1$ intercepts The $x$ axis.

# Functions of one variable

Reasoning
13

#### Scale balance

How heavy is the boy?

# Unassigned

Modeling
9

#### Side length of a rectangle

Which of the following equations fits the picture if the goal is to calculate the length of x?

# Unassigned

Reasoning
9

#### Differential of the function arcsin

Find the differential of the function $y=\arcsin(\frac{u}{v})$ where $u$ and $v$ are differentiable functions of $x$.

# Functions of one variable

Training
13