THE SINE FUNCTION (SIN)
Sine function is an odd function. Trigonometric Ratios in a Triangle
Definition of sinα in a Triangle is the following statement:
For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle.
If we simplify we get a formula which says:
It is shown in a diagram below.
We can see immediately that this definition has a weak point. It does not tell us exactly which right triangle to draw. There are many right triangles, large ones and small ones that include a given angle α. The Law of Sines
In a triangle, there are two expressions for altitude (height on one of the sides). I …show more content…
Then formula is cosα=b/c=(adjacent leg)/hypotenuse
Here is also a diagram for easier understanding. The Law of cosines
The law of cosine first appears in Euclid’s Elements, which is one of the very first textbook of geometry. If we got a triangle ABC and if angle β is an acute angle then we use the following formula to calculate sides:
We can use the law of cosines in a triangle to calculate angles and sides of triangle. For that to happen we must already know two sides and an angle between this two sides. If we got this information then we can get other side with these following formulas:
But we can also use the law of cosine if we have information on how long all 3 sides are. Then we remodel our formula to these following formulas:
The law of cosine can be easy to prove with help of Pythagorean Theorem, which we use twice.
Definition: The cosine of an obtuse angle is the cosine of its supplement multiplied by -1. Graph of the cosine function
We can calculate the zeros, maximums and minimums of cosine function with following
Sine function is an odd function. Trigonometric Ratios in a Triangle
Definition of sinα in a Triangle is the following statement:
For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle.
If we simplify we get a formula which says:
It is shown in a diagram below.
We can see immediately that this definition has a weak point. It does not tell us exactly which right triangle to draw. There are many right triangles, large ones and small ones that include a given angle α. The Law of Sines
In a triangle, there are two expressions for altitude (height on one of the sides). I …show more content…
Then formula is cosα=b/c=(adjacent leg)/hypotenuse
Here is also a diagram for easier understanding. The Law of cosines
The law of cosine first appears in Euclid’s Elements, which is one of the very first textbook of geometry. If we got a triangle ABC and if angle β is an acute angle then we use the following formula to calculate sides:
We can use the law of cosines in a triangle to calculate angles and sides of triangle. For that to happen we must already know two sides and an angle between this two sides. If we got this information then we can get other side with these following formulas:
But we can also use the law of cosine if we have information on how long all 3 sides are. Then we remodel our formula to these following formulas:
The law of cosine can be easy to prove with help of Pythagorean Theorem, which we use twice.
Definition: The cosine of an obtuse angle is the cosine of its supplement multiplied by -1. Graph of the cosine function
We can calculate the zeros, maximums and minimums of cosine function with following