Trigonometrical Ratios
The ratio between the lengths of a pair of two sides of a right angled triangle is called a trigonometric ratio.
The three sides of a rightangled triangle give six trigonometric ratios; namely sine, cosine, tangent, cotangent, secant and cosecant. In short, these ratios are written as sin, cos, tan , cot, sec and cosec respectively.
In a right angledtriangle with acute angle A, the trigonometric ratios are defined as:
sin A = perpendicular / hypotenuse
cos A = base/ hypotenuse
tan A = perpendicular/ base
cosec A = hypotenuse/ perpendicular
sec A = hypotenuse/ base
cot A = base/perpendicular
The ratios cosec A, sec A and cot A are the reciprocal of the ratios sin A, cos A and tan A respectively.
The trigonometric ratios sin A, cos A, tan A, cot A, sec A, and cosec A are also known as trigonometric functions of A.
sin 0° = 0, cos 0° = 1, tan 0°= 0
sin 90° = 1, cos 90° = 0, tan 90°= not defined
A trigonometric equation is an equation that has one or more trigonometric ratios or trigonometric functions of an unknown angle. Solving a trigonometric equation involves steps to find the value of an unknown angle that satisfies the given equation.
Keywords: Trigonometric Ratios of Specific Angles
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Q1
If x = 15°, evaluate:
4. sin 2x. sin 3x. cos 3x. cos 4x
Marks:2Answer:

Q2
Solve:
2.sin x + cosec x  3 = 0Marks:5Answer:

Q3
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Q4
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Q5Marks:1
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