Sine (sin): A ratio of the lengths of sides in a right triangle, specifically the length of the side opposite the angle divided by the length of the hypotenuse. It provides a fundamental relationship between an angle and the side lengths in right-angled triangles.
Cosine (cos): A ratio of the lengths of sides in a right triangle, specifically the length of the side adjacent to the angle divided by the hypotenuse. It establishes a key connection between an angle and the side lengths in right triangles.
Tangent (tan): A ratio of the lengths of sides in a right triangle, specifically the length of the side opposite the angle divided by the length of the side adjacent to the angle. It relates an angle to the ratio of two sides in right triangles.
Reciprocal functions: These are functions derived from the basic trig functions by taking their reciprocals. Cosecant (csc) is the reciprocal of sine, secant (sec) is the reciprocal of cosine, and cotangent (cot) is the reciprocal of tangent. They extend the basic relationships and are useful in various identities.
1. What is the key characteristic that defines the ratios of sine, cosine, and tangent in the trigonometric functions table?
2. What is the primary role of sine values in trigonometry?
3. After how many degrees does the tangent function repeat its values?
Trigonometric functions table — purpose?
Summarizes sine, cosine, tangent ratios for key angles.
Sine — definition?
Opposite side over hypotenuse in a right triangle.
Tangent — role?
Opposite over adjacent sides; slope of a line.
Non-calculator table — angles?
Includes exact values for 30°, 45°, 60°.
Sin 30 — value?
1/2.
Sin 45 — value?
√2/2.
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