# Online Trigonometry Tutoring: Trigonometric Identities

Home | Online Math Tutoring | Online Trigonometry Tutoring | **Basic Trigonometric Identities**

**Simplify trigonometry.**

Our expert and qualified** **trigonometry tutors understand your problems and guide you towards better grades in trigonometry. Our aim is to help the student understand concepts in trigonometry and master the techniques of solving problems quickly with confidence.

## Learn Trigonometric Identities from certified Online Trigonometry tutor:

**Identity** is an equation which is always true for all defined values

Tangent and cotangent functions can be expressed in terms of the sine and cosine functions

tan x =

cot x =

These reciprocals are used to find the value of trig functions:

sin x = ; cosec x =

cos x = ; sec x =

tan x = ; cot x =

**Pythagorean Identities is to help simplify trigonometric expressions.****Simplifying trigonometric expressions to create a factorable expression used to find missing trigonometric values.****Used to find missing trigonometric values**

+ = 1

+ 1 =

1 + =

**Example 1**

**Prove that tan y/sin y = sec y**

Expressing it in terms of sin y or cos y, we get

LHS = tan y × 1/sin y

= (sin y/cos y) × 1/sin y (tan A = sin A/cos A)

= 1/cos y

= sec y (since 1/cos A = sec A)

= RHS

**Example 2**

**Verify the identities**

1/sec^{2}a = sin^{2}a . cos^{2}a + cos^{4}a

RHS = cos^{2}a (sin^{2}a + cos^{2}a)

= cos^{2}a (1) {we know, sin^{2}a + cos^{2}a =1}

= cos^{2}a

LHS = 1/sec^{2}a = 1/(1/ cos^{2}a) = cos^{2}a

**Check Point**

Problem 1. If sinθ = 2/3, find cosθ.

Problem 2. If cos θ = 5/11 and sin θ = 9/11, what is the value of tan θ?

Problem 3. Express sin 67° + cos 65° in terms of trigonometric ratios of angle between 0 and 45 degrees.

Problem 4. If cos θ = .7, find the value of sec θ.

##### Answer Key

1. cos θ =

2. tan θ = 9/5

3. cos 23° + sin 25°

4. sec θ = 10/7

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