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The answer depends on how sine and cosine are defined: as ratios in right angled triangles, as infinite series or some other way (there are many). The explanation is easiest for definitions based on right angled triangles. Since this browser does not allow graphics, the explanation will be simpler to follow if you just sketch a rough triangle.
Suppose you have triangle ABC which is right angled at C.
Then, since angle A + angle B + angle C = 180 degrees,
angle A + angle B = 90 deg.
That is, A and B are complementary angles.
Now consider the ratio of the sides BC/AB.
AB is the hypotenuse of the triangle.
From the perspective of angle A, BC is the opposite side so the above ratio is sin(A).
From the perspective of angle B, BC is the adjacent side so the above ratio is cos(B).
Thus sin(A) = cos(B).
Similarly, if you consider AC/AB you can show that cos(A) = sin(B).
What else can I help you with?
What shapes opposite angles are congruent?
Opposite angles are congruent in any pair of intersecting lines, such as those formed by two straight lines crossing each other. When two lines intersect, they create four angles, and the angles that are opposite each other (vertical angles) are always equal in measure. This property holds true regardless of the angle sizes, making vertical angles congruent in all cases of intersection.
Are corresponding angles of similar quadrilaterals congruent?
Yes, corresponding angles of similar quadrilaterals are congruent. Similar quadrilaterals have the same shape but may differ in size, which means their corresponding angles remain equal. This property holds true for all similar figures, not just quadrilaterals. Thus, if two quadrilaterals are similar, their corresponding angles will always be congruent.
How are a square and triangle different?
A square has four sides whereas a triangle has only three. A square holds 360 degrees, whereas a triangle only holds 180 degrees. A square has all four sides even with 90 degrees in each whereas a triangle angles/sizes vary.
What is the sum of the exterior angles of a 14-sided figure?
The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. Therefore, for a 14-sided figure, the sum of the exterior angles is also 360 degrees. This holds true for all polygons, whether they are regular or irregular.
What is the equation for angles of triangles?
The sum of the interior angles of a triangle is always 180 degrees. This can be expressed as the equation: ( A + B + C = 180^\circ ), where ( A ), ( B ), and ( C ) are the measures of the three interior angles of the triangle. This property holds true for all types of triangles, whether they are acute, obtuse, or right triangles.
What is the name of the layer over Los angles that holds in the smog?
The layer of air over L.A. that holds in smog is called an inversion layer.
What type of bond holds one nitrogen base to its complementary base?
I Believe the answer is sequence of nitrogen bases. 70 Year old woman in 5th Grade , i think i know this.
Do the diagonals of a square bisect the angles?
Yes, the diagonals of a square bisect the angles. This means that each diagonal divides the angles at the vertices into two congruent angles. In a square, all angles are right angles (90 degrees), so each diagonal divides the right angles into two equal angles of 45 degrees each. This property holds true for all squares.
What hold a long-distance relationship together?
What holds a long distant relationship together is COMMUNICATION AND TRUST..even in a not distant relationship there has to be both of those there or there is no real relationship.
What holds complementary bases together?
Hydrogen bonds hold complementary bases together in DNA molecules. These hydrogen bonds form between adenine (A) and thymine (T), as well as between guanine (G) and cytosine (C). The specific base pairing is crucial for the overall structure and function of DNA.
What shapes opposite angles are congruent?
Opposite angles are congruent in any pair of intersecting lines, such as those formed by two straight lines crossing each other. When two lines intersect, they create four angles, and the angles that are opposite each other (vertical angles) are always equal in measure. This property holds true regardless of the angle sizes, making vertical angles congruent in all cases of intersection.
For very small angles the focal length of a concave mirror is?
For very small angles, the focal length of a concave mirror is approximately half of the radius of curvature of the mirror. This is known as the mirror equation and holds true for small angles under the paraxial approximation.
What relationship does Thanksgiving have with the Puritans?
Tradition holds that it was a Puritan celebration of their first harvest in the New World.
Was the god Odin a Christian?
No. Odin was of Norse mythology and holds no relationship to God or Jesus Christ.
Is a boyfriend considered a relative?
no if you havent married eachother or had children, there just your boyfriend... its a not so serious relationship but holds seriousness within to maintain a healthy relationship
Are corresponding angles of similar quadrilaterals congruent?
Yes, corresponding angles of similar quadrilaterals are congruent. Similar quadrilaterals have the same shape but may differ in size, which means their corresponding angles remain equal. This property holds true for all similar figures, not just quadrilaterals. Thus, if two quadrilaterals are similar, their corresponding angles will always be congruent.
How are a square and triangle different?
A square has four sides whereas a triangle has only three. A square holds 360 degrees, whereas a triangle only holds 180 degrees. A square has all four sides even with 90 degrees in each whereas a triangle angles/sizes vary.
