sin(θ)=opp/hyp
In trigonometry, the sine function relates the ratio of the lengths of the side opposite an angle (opp) to the length of the hypotenuse (hyp) of a right triangle
In trigonometry, the sine function relates the ratio of the lengths of the side opposite an angle (opp) to the length of the hypotenuse (hyp) of a right triangle. This relationship is given by the equation sin(θ) = opp/hyp.
To better understand this equation, let’s consider a right triangle:
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hypo (hyp) | /|
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angle (θ) ______|______ side opposite (opp)
In this triangle, we have an angle θ, a side opposite that angle (opp), and a hypotenuse (hyp). The ratio of the length of the side opposite to the hypotenuse is represented by sin(θ).
For example, let’s say we have a right triangle with an angle of 30 degrees and a side opposite that angle of length 6 units. The length of the hypotenuse can be calculated using the sine function:
sin(30°) = opp/hyp
Since sin(30°) is equal to 0.5 (a common value you will encounter in trigonometric tables or calculators), we can rearrange the equation to solve for hyp:
0.5 = 6/hyp
Now, we can multiply both sides of the equation by hyp to isolate it:
0.5 * hyp = 6
Dividing both sides of the equation by 0.5 gives us:
hyp = 6 / 0.5 = 12
Therefore, in this triangle, the length of the hypotenuse is 12 units.
The sine function is a fundamental trigonometric function that helps us understand the relationship between angles and the sides of a right triangle. It is commonly used in fields such as physics, engineering, and navigation, among others.
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