Introduction :

Trigonometry is one of the most important and oldest topics in modern mathematics. The collection of formulas in the trigonometry is usually called as trigonometric function and identities. The list trigonometric function and identities are developed to help in the measurement of triangles and their angles. In online, many websites provide online tutoring using tutors. Those tutors interact with students while tutoring in live and solve the problems related to all subjects. One of the most famous and affordable tutoring site is “Tutorvista.com”, which helps students with thousands of tutors. In this article, we are going to learn about, trigonometric functions identities tutoring.

## Trigonometric functions identities tutoring: - Basic trigonometric functions identities

The list of basic trigonometric functions identities and functions are shown below,

**The 6 trigonometric functions:**

Sin `theta = (Opp)/ (hyp)`

Cos `theta = (adj)/ (hyp)`

Tan theta = (Opp)/ (adj)

Csc `theta = (hyp)/ (opp)`

Sec `theta = (hyp)/ (adj)`

Cot `theta = (adj)/(opp)`

**Sum or difference of two angles:**

sin (a ± b ) = sin a cos b ± cos a sin b

cos(a ± b) = cos a cos b ± sin a sin b

tan(a ± b) = `(tan a +- tan b)/ (1 +- tan a tan b)`

**Co-function identities:**

Sin `(pi/2-theta) ` = cos `theta`

Cos `(pi/2-theta)`= sin `theta`

Tan `(pi/2-theta)` = cot `theta`

Csc `(pi/2-theta) ` = sec` theta`

Sec `(pi/2-theta)` = csc `theta`

Cot `(pi/2-theta)` = tan `theta`

**Power reducing formulas:**

Sin^{2} `theta = (1-cos 2theta)/2`

Cos^{2} `theta = (1+cos 2theta)/2`

Tan^{2}` theta = (1-cos 2theta)/(1+cos 2theta)`

**Half angle formulas:**

Sin^{2} `theta = 1/2(1-cos 2theta)`

Sin `theta/2 = +-sqrt((1-cos theta)/2)`

tan `theta/2 = +- sqrt((1- cos theta)/(1+ cos theta)) = sin theta/(1+cos theta) = (1-cos theta)/ sin theta`

Cos^{2} `theta = 1/2(1+cos 2theta)`

Cos `theta/2 = +-sqrt((1+cos theta)/2)`

## Trigonometric functions identities tutoring: - Examples

**Example 1: **

cos (2x) = 0.8 and 2x is in quadrant I. Find the value of csc (x).

**Solution:**

Using the identity cos (2x) = 2 cos^{2} x - 1

0.8 = 2cos ^{2}x - 1

0.8 = 2cos ^{2}x - 1

cos ^{2}x = 0.9

Now, using sin^{2} x + cos^{2} x = 1

sin x = `sqrt(1-0.9)`

We know that, csc x = `1/sin x `

csc (x) = `1/sqrt(0.1)`

**The answer is 1/sqrt(0.1)**

**Example 2:**

Evaluate tan^{2} 30

**Solution:**

Tan^{2} `theta` = `(1-cos 2theta)/(1+cos 2theta)`

Tan^{2} 30 = `(1-cos 2(30))/(1+cos 2(30))`

= `(1-cos 60)/(1+cos 60)`

= `(1-0.5)/(1+0.5)`

= `0.5/1.5`

= 0.33

**The answer is 0.33 **