Here are some examples of how the basic trigonometric functions can be used to solve problems involving triangles:
These identities are very useful for simplifying trigonometric expressions and solving trigonometric equations.
Trigonometric equations are equations that involve trigonometric functions. Some examples of trigonometric equations include:
Solving trigonometric equations is the process of finding all the solutions to a trigonometric equation. There are many different methods for solving trigonometric equations, and the best method to use will depend on the specific equation. Some common methods for solving trigonometric equations include:
Factoring trigonometric equations is the process of breaking a trigonometric equation down into a product of simpler trigonometric expressions. Factoring trigonometric equations can be helpful for solving trigonometric equations, and it can also be helpful for simplifying trigonometric expressions. For example, the equation sin x + cos x = 1 can be factored as sin x + cos x = (sin x + cos x)(1) = sin x cos x + 1.
Reciprocal trigonometric equations are equations that involve the reciprocals of the trigonometric functions. Reciprocal trigonometric equations can be solved using the same methods as regular trigonometric equations. For example, the equation 1/sin x = 1/cos x can be solved as sin x = cos x.
Double angle trigonometric equations are equations that involve the double angle formulas for the trigonometric functions. Double angle trigonometric equations can be solved using the double angle formulas, or they can be solved by converting them to regular trigonometric equations. For example, the equation sin 2x = 1 can be solved using the double angle formula for sin x, which is sin 2x = 2 sin x cos x.
Half angle trigonometric equations are equations that involve the half angle formulas for the trigonometric functions. Half angle trigonometric equations can be solved using the half angle formulas, or they can be solved by converting them to regular trigonometric equations. For example, the equation tan x = √3 can be solved using the half angle formula for tan x, which is tan x = 2 tan(x/2) / 1  tan^{2}(x/2).
Q1: A tower has a height of 50 m. It has an angle of elevation from two points on the ground level on its opposite sides are 30 degree and 60 degree respectively. Calculate the distance between two points.
(a)110.97 m
(b) 107.56 m
(c) 115.47 m
(d) 120.93 m
(e) None of the above
Ans: c
Q2: The value of 32cot2π/4  8sec2π/3 + 8cos3π/6
(a) √3
(b) 2√3
(c) 3
(d) 3√3
(e) None of the above/More than one of the above.
Ans: d
320 videos195 docs244 tests

Trigonometric Ratio's Video  25:24 min 
Complementary Angles Video  23:22 min 
Using One Finding other Angle Video  26:54 min 
1. What are the basic trigonometric functions? 
2. How is the sine function defined? 
3. What is the cosine function used for? 
4. How can the tangent function be calculated? 
5. What are some practical applications of trigonometric functions? 
320 videos195 docs244 tests

Trigonometric Ratio's Video  25:24 min 
Complementary Angles Video  23:22 min 
Using One Finding other Angle Video  26:54 min 

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