If csc θ=8/7, which equation represents cotθ

1 answer:

6 0

Sin θ = opposite leg/hypotenuse
csc θ = hypotenuse /opposite leg =8/7

cot θ = adjacent leg/opposite leg

hypotenuse =8
opposite leg =7
We need to find adjacent leg.

(Opposite leg)² +(adjacent leg)² = hypotenuse²
7² + (adjacent leg)² =8²
(adjacent leg)² = 64 - 49
(adjacent leg)² = 15

adjacent leg=+/-√15
WE need only positive root,
so adjacent leg =√15

cot θ = √15/7 or 0.5533

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<h3>Explanation</h3>

A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.

Line Test

Draw a vertical line. Make sure that a line passes through a graph.
See if a line intercepts a graph more than one point or just only one.

Result

If a line intercepts a graph more than one point, it is not a function.

However, if a line only intercepts a graph just one point, it is indeed a function.

The given graph from the question is a function because it passes line test.

Domain and Range

Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.

Range is the set of all y-values. We only focus on y-value or y-axis for Range.

Determine Domain from Graph

We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.

Determine Range from Graph

Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.

From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.

<h3>Answer</h3>

 $\begin{cases} x \in \mathbb{R} \\ y \geqslant 0 \end{cases}$ 