4. Answer the following questions:
1. What is a trigonometric function?
2. What lines in any right triangle are called sides?
3. What is called the tangent of the angle?
4. What is called the cotangent?
5. What is the sine of an angle?
6. What is the cosine of an angle?
7. What is the secant of an angle?
8. What is the cosecant of an angle?
5. Translate into Russian:
We find that the values of the right triangle ratios depend only on angles and that to each different angle there corresponds a different set of those values. Any number or quantity is called a function of that second number or quantity. Therefore, the right triangle ratios are functions of the acute angles of the triangle.
6. Read and translate the Laws of Sines and Cosines. Learn them by heart:
The Law of Sines. In a triangle any side is to any other side as the sine of the angle opposite the first side is to the sine of the angle opposite the other side; or, if a and b be the sides, and A and B the angles opposite them:
a/b = sin A/ sin B
The Law of Cosines. In a triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle; or if a, b and c be the sides and the angle opposite side a be denoted A, then: a2 = b2+ c2 - 2bc cos A.
7. Translate into English:
Тангенсом угла называется отношение синуса угла к косинусу этого угла.
Котангенсом угла называется отношение косинуса угла к синусу этого угла. Остальные тригонометрические функции - это синус, косинус, секанс и косеканс.
Синус острого угла - это отношение стороны, противоположной этому углу, к гипотенузе.
Косинус - это отношение смежной стороны к гипотенузе.
Секанс - это отношение гипотенузы к стороне, смежной с углом.
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