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4 years ago

4 times the sum of a number and 5 is 1 less than the same number

Mathematics

1 answer:

hodyreva [135]4 years ago

7 0

x = a number

4(x + 5) = x - 1

Now, let's distribute the 4

4x + 20 = x - 1

Subtract x and 20 from both sides.

3x = -21

Divide both sides by 3

x = -7

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Trigonometry Trigonometric Functions Given: Cos θ = (3/5), Find: Csc θ

torisob [31]

The value of $\csc \theta$ is $\frac{5}{4}$

Explanation:

Given that the function $cos \ \theta$ is $cos \ \theta= \frac{3}{5}$

We need to determine the value of $\csc \theta$

The value of Opposite side of the triangle:

The formula for $cos \ \theta$ is given by

$cos \ \theta= \frac{adj}{hyp}=\frac{3}{5}$

The value of opposite side can be determined using the formula,

$opp=\sqrt{hyp^2-adj^2$

$opp=\sqrt{5^2-3^2}$

$opp=\sqrt{25-9}$

$opp=\sqrt{16}=4$

Thus, the value of opposite side is 4

The value of $sin \ \theta$ :

The formula for $sin \ \theta$ is given by

$sin \ \theta= \frac{opp}{hyp}$

Substituting the values, we have,

$sin \ \theta= \frac{4}{5}$

Thus, the value of $sin \ \theta$ is $\frac{4}{5}$

The value of $\csc \theta$ :

The formula for $\csc \theta$ is given by

$csc \ \theta=\frac{1}{sin \ \theta}$

Substituting the values, we have,

$csc \ \theta=\frac{1}{\frac{4}{5}}$

$csc\ \theta= \frac{5}{4}$

Thus, the value of $\csc \theta$ is $\frac{5}{4}$

Hence, the value of $\csc \theta$ is $\frac{5}{4}$

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3 years ago