Trigonometric Ratios of Allied Angles MCQ - Practice Questions & Answers

Solve by difficulty

MEDIUM

Evaluate the value of $\mathrm{ tan\ 60^{\circ}+cot\ 60^{\circ}}$ ?

$\mathrm{\frac{2}{\sqrt{3}}}$

$\mathrm{\frac{4}{\sqrt{3}}}$

$\mathrm{\frac{1}{\sqrt{3}}}$

$\mathrm{\frac{3}{\sqrt{3}}}$

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The value of $\mathrm{ \frac{sin\left ( 90^{\circ}+\theta \right )sin\left ( 180^{\circ}+\theta \right )}{cos\left ( 90^{\circ}+\theta \right )}}$ is?

$\mathrm{cos\ \theta }$

$\mathrm{sin\ \theta}$

$\mathrm{tan\ \theta}$

$\mathrm{cot \theta}$

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Concepts Covered - 2

Allied Angles (Part 1)

Allied Angles (Part 1)

Two angles are called allied if their sum or difference is a multiple of π/2

sin (90⁰ - θ) = cos (θ)
cos (90⁰ - θ) = sin (θ)
tan (90⁰ - θ) = cot (θ)
csc (90⁰ - θ) = sec (θ)
sec (90⁰ - θ) = csc (θ)
cot (90⁰ - θ) = tan (θ)

sin (90⁰ + θ) = cos (θ)
cos (90⁰ + θ) = - sin (θ)
tan (90⁰ + θ) = - cot (θ)
csc (90⁰ + θ) = sec (θ)
sec (90⁰ + θ) = - csc (θ)
cot (90⁰ + θ) = - tan (θ)

Allied Angles (Part 2)

Allied Angles (Part 2)

sin (180⁰ - θ) = sin (θ)
cos (180⁰ - θ) = - cos (θ)
tan (180⁰ - θ) = - tan (θ)
csc (180⁰ - θ) = csc (θ)
sec (180⁰ - θ) = - sec (θ)
cot (180⁰ - θ) = - cot (θ)

sin (180⁰ + θ) = - sin (θ)
cos (180⁰ + θ) = - cos (θ)
tan (180⁰ + θ) = tan (θ)
csc (180⁰ + θ) = - csc (θ)
sec (180⁰ + θ) = - sec (θ)
cot (180⁰ + θ) = cot (θ)

AID TO REMEMBER

All the trigonometric function of a real number of the form 2n(π/2) ± x ( n ∈ I) (i.e. an even multiple of π/2 ± x) is numerically equal to the same function of x, with sign depending on the quadrant in which terminal side of the angles lies.

For example: cos (π + x) = cos (2(π/2) + x) = - cos (x), -ve sign chosen because (π + x) lies in 3rd quadrant and ‘cos’ is -ve in third quadrant.

All the trigonometric function of a real number of the form (2n + 1)π/2 ± x ( n ∈ I) (i.e. an even multiple of π/2 ± x) is numerically equal to the co-function of x, with sign depending on the quadrant in which terminal side of the angles lies.

Note that ‘sin’ and ‘cos’ are co-functions of each other, ‘tan’ and ‘cot’ are co-function of each other and ‘sec’ and ‘cosec’ are co-function of each other.

For example: sec (π/2 +x ) = - cosec (x), as (π/2 +x) lies in the 2nd quadrant and ‘sec’ is -ve in 2nd quadrant.