Trigonometry refers to the statement that includes the relationship between the sides and right angles. Major trigonometric ratios are sin, cos, cot, tan, cosine, sec, etc.
Main functions of Trigonometry
Generally, there are three main functions of trigonometry. These functions are given below:
Sin
Cos
Tan
Even or Odd functions of trigonometry
The odd trigonometric functions are the functions that refer to f(-x) = -f(x) and it is also symmetric to its origin. Whereas the even trigonometry functions are the functions in which f(-x) = f(x) and it is considered symmetric to the y-axis.
The following are some of the odd and even trigonometric functions:
Sin (-x) = - Sin x
Tan (-x) = -Tan x
Cos (-x) = Cos x
Csc (-x) = - Csc x
Cot (-x) = -Cot x
Sec (-x) = Sec x
Formulas of trigonometric functions
sin²θ + cos²θ = 1
Sec2θ = tan2θ + 1
Cosec2θ = cot2θ + 1
sin 2θ = 2 sin θ cos θ
cos²θ – sin²θ = cos 2θ
2 tan θ / (1 – tan²θ) = tan 2θ
(cot²θ – 1) / 2 cot θ = cot 2θ
Identities of trigonometry
a2 + b2 – 2ab cos C = c2
b2 + c2 – 2bc cos A = a2
a2 + c2 – 2ac cos B = b2
These are all trigonometric functions, along with their identities.
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Free Introduction to Trigonometry Olympiad Questions for Class 10
5 questions to build confidence. Choose an answer, then explore the explanation.
01
Mia, who is a teacher, needs pencils for the upcoming school year, as she gives them out to students throughout the year. The pencils come in packages of 5, each package costing $2.00. The store only has 30 packages. If the function P(x) represents how many pencils Mia is able to buy with x dollars, what is the best domain for this function?
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Answer: A. {x in RR | 0 <= x <= 60}
She can spend from $0 up to $60 total (30 packages × $2).
02
If theta is the angle formed between a line from the origin to the point (-3,5) and the x axis, find sin theta.
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Answer: A. sin theta = 5/sqrt(34)
The point (-3,5) gives r = sqrt(34), so sin θ = opposite/hypotenuse = 5/sqrt(34).
03
What is the explicit form of the sequence defined by a_1 = 1/2; \ \ a_n = 1/2 a_{n-1}, \ n>1 ?
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04
An angle that measures exactly 90 degrees.
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05
Which of these is not a type of angle?
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