Let sin ? = 4/5, and cos ? = ?3/5, and find the indicated value

1 answer:

4 0

Let the unknown angle be x.
That is
sin x = 4/5
cos x = 3/5

By drawing a right triangle in the first quadrant,
hypotenuse = 5
Adjacent side = 3
opposite side = 4

That is tan x = 4/3
From the calculator,
x = arctan(4/3) = 53 deg (nearest integer)

Answer: 53 deg. (nearest integer)

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Solve the x 1/3x + 5> 10

kotykmax [81]

Answer:

The solution to the inequality is:

$\frac{1}{3}x+5>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>15\:\\ \:\mathrm{Interval\:Notation:}&\:\left(15,\:\infty \:\right)\end{bmatrix}$

The solution graph is also attached below.

Step-by-step explanation:

Given

We are given the expression

$\frac{1}{3}x+5>10$

To determine

Solve for x

Given the expression

$\frac{1}{3}x+5>10$

Subtract 5 from both sides

$\frac{1}{3}x+5-5>10-5$

Simplify

$\frac{1}{3}x>5$

Multiply both sides by 3

$3\cdot \frac{1}{3}x>5\cdot \:3$

Simplify

$x>15$

Thus, we conclude that:

$x>15$

Therefore, the solution to the inequality is:

$\frac{1}{3}x+5>10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>15\:\\ \:\mathrm{Interval\:Notation:}&\:\left(15,\:\infty \:\right)\end{bmatrix}$

The solution graph is also attached below.