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Chapter Analysis
Intermediate27 pages • EnglishQuick Summary
The chapter on Trigonometric Functions in Class 11 Mathematics delves into the extension of trigonometric ratios to any angle, encompassing radian measures. It covers trigonometric identities, the relationship between degree and radian measures, and the behavior of trigonometric functions across various quadrants. The chapter also introduces formulas for trigonometric functions involving the sum and difference of angles. It lays a foundational understanding required for solving complex trigonometric equations.
Key Topics
- •Extension of trigonometric functions to any angle
- •Radian and degree measures
- •Trigonometric identities
- •Trigonometric functions of sum and difference of angles
- •Domain and range of trigonometric functions
- •Behaviour of trigonometric functions across quadrants
Learning Objectives
- ✓Understand the relationship between degree and radian measures
- ✓Learn the trigonometric identities and their applications
- ✓Explore trigonometric functions in various quadrants
- ✓Apply trigonometric formulas to solve complex equations
- ✓Develop proficiency in converting between different angle measures
Questions in Chapter
Find the radian measures corresponding to the following degree measures: (i) 25°, (ii) – 47°30', (iii) 240°, (iv) 520°.
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Find the degree measures corresponding to the following radian measures: (i) 11/16, (ii) – 4, (iii) 5π/3, (iv) 7π/6.
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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
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In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of the minor arc of the chord.
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Additional Practice Questions
Convert 120° to radians.
easyAnswer: To convert degrees to radians, multiply by π/180. Thus, 120° = 120 * π/180 = 2π/3 radians.
Prove the identity: sin^2 x + cos^2 x = 1.
mediumAnswer: Using the unit circle, for any angle x, the x-coordinate is cos x and the y-coordinate is sin x. The radius of the unit circle is 1. Thus, (cos x)^2 + (sin x)^2 = 1.
Find the exact value of sin(45° + 45°).
mediumAnswer: Using the identity sin(x + y) = sin x cos y + cos x sin y, and knowing sin 45° = cos 45° = √2/2, sin(90°) = √2/2 * √2/2 + √2/2 * √2/2 = 1.
If cos x = 1/2, find the value of x.
mediumAnswer: cos x = 1/2 for x = 60° and x = 300°, within the range of 0° to 360°.
Determine tan(π/4).
easyAnswer: The value of tan(π/4) is 1, since it corresponds to a 45° angle where the opposite and adjacent sides are equal.
Prove that cos(–x) = cos x.
easyAnswer: Cosine is an even function, meaning the graph is symmetric with respect to the y-axis: cos(–x) = cos x.
Find the values of the trigonometric functions if tan x = 1, where 0 < x < π.
mediumAnswer: If tan x = 1, then x = π/4 (45°) in the first quadrant, where sin x = cos x = √2/2.
Evaluate sin(–30°).
easyAnswer: The sine function is odd, so sin(–30°) = –sin(30°) = –1/2.