March 4, 2017 Help

Online trigonometry math help:

Trigonometry deals with triangles and their properties. Properties of triangles revolve around its sides and interior angles and the relationship among them. The phostulates and theorems in trigonometry are the basic building blocks of the study and is helpful in determining various scales of real life figures having triangular shape. Trigonometry like any other branch is based on pure logic and extension of it.

Online Trigonometry Math Help – Example Problems:

Example 1:

If sin 3A = cos (A- 26°), where 3A is an acute angle, find the value of A.

Solution:

We are given that 3A = cos (A – 26°).

since sin 3A = cos (90° – 3A) = cos (90° – 3A), we can write (1) as

cos (90° – 3A) = cos (A – 26°)

since 90° – 3A and A – 26° are both acute angles,

Therefore, 90° – 3A = A – 26°

Which gives A = 29°

Example 2:

Prove that sec A (1 – sin A) (sec A + tan A) = 1.

Solution:

LHS = sec A (1 – sin A) (sec A + tan A) = ‘1/((cos A) (1-sin A))’ ‘1/(cos A)’ + ‘(sin A)/(cos A))’

= ‘((1-sinA) (1+sinA))/ (cos^2A)’

= ‘(1-sin^2A)/(cos^2A)’

=’ (cos^2A)/(cos^2A) ‘ = 1 RHS

Example 3:

Cos 2x = cos^2 x – sin^2 x = 2 cos^2 x -1 = 1 – 2 sin^2 x = ‘(1-tan^2 x)/ (1+tan^2 x)’

Solution:

We know that cos (x+y) = cos x cos y – sin x sin y

Replacing y by x, we get

Cos 2x = cos^2 x – sin^2 x = 2 cos^2 x – 1

= cos^2 x – (1 – cos^2 x) = 2 cos^2 x – 1

Again, cos 2x = cos^2 x – sin^2 x

= 1 – sin^2 x – sin^2 x = 1 – 2 sin^2x

We have cos 2x = cos^2 x – sin^2 x = ‘(cos^2 x-sin^2 x)/ (cos^2 x + sin^2 x)’

Dividing each term by cos^2 x, we get

Cos 2x = ‘(1-tan^2 x)/ (1+tan^2 x)’

Online Trigonometry Math Help – Practice Problems:

Problem 1: Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Problem 2: Prove that ‘(cot A-cos A)/ (cotA+cos A)’ = ‘(cosec A-1)/(cosec A+1)’

Problem 3: sin 2x = 2 sin x cos x = ‘(2 tan x) / (1+tan^2 x)’

Online trigonometry math help – answer key:

Problem 1: tan 5° + sin 15°

Problem 2: ‘(cosec A-1)/(cosec A+1)’ = RHS

Problem 3: ‘(2 tan x) / (1+tan^2 x)’

More Practice Problems

Example 1:

Express the ratios cos A, tan A and sec A in terms of sin A.

Solution:

Since cos^2 A + sin^2 A = 1

Therefore, cos^2 A = 1 – sin^2 A

Cos A = ‘+- sqrt(1- sin^2 A)’

This gives cos A = ‘sqrt(1-sin^2 A)’

Hence, tan A = ‘(sin A)/ (cos A)’

= ‘(sin A)/ sqrt(1-sin^2A)’ and sec A = ‘1/(cos A)’ = ‘1/sqrt(1-sin^2 A)’

Example 2:

Prove that sec A (1 – sin A) (sec A + tan A) = 1

Solution:

LHS = sec A (1 – sin A) (sec A + tan A) = [‘1/(cos A)’ ] (1 – sin A) ‘[ 1/(cos A) + (sin A)/( cos A)]’

= ‘((1-sinA) (1+sin A))/ (cos^2A)’ = ‘(1-sin^2A)/ (cos^2 A)’

= ‘(cos^2A)/ (cos^2A) ‘ = 1 RHS

Example 3:

Show that cos^4 A – sin^4 A = 1 – 2 sin^2 A

Solution:

Sec2 A + cosec2 A = ‘1/(cos^2A)’ +’ 1/(sec^2A)’

‘(sin^2A + cos^2A)/ (cos^2A * sin^2A)’ =cos A. cosec A

= ‘(cos A)/ (sin A)’ = cot A = ‘sqrt(cosec^2 A-1)’

Example 4:

If a sin^2 ‘theta’ + b cos^2 ‘theta’ = c, show that tan^2 ‘theta’ = ‘(c-b)/ (a-c)’

Solution:

a sin^2 ‘theta’ + b cos^2 ‘theta’ = c

Dividing both sides by cos^2 ‘theta’ , we get a tan^2 ‘theta’ + b = c sec2 ‘theta’

a tan^2 (a – c) = c – b

tan^2 ‘theta’ = ‘(c-b)/ (a-c)’

Trigonometric examples tutoring – practice problems:

Problem 1: If x = a cos ‘theta’ + b sin ‘theta’ and y = a sin ‘theta’ – b cos ‘theta’ , show that x^2 + y^2 = a^2 + b^2

Problem 2: sin^4 A – cos^4 A = 1 – 2cos^2 A

Trigonometric examples tutoring – answer key:

Problem 1: a^2 + b^2

Problem 2: 1 – 2cos^2 A

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