Select Page

Online Trigonometry Tutoring: 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 = \frac{sin x}{cos x}

cot x = \frac{cos x}{sin x}

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

sin x = \frac{1}{cosec x}; cosec x = \frac{1}{sin x}

cos x = \frac{1}{sec x}; sec x = \frac{1}{cos x}

tan x = \frac{1}{cot x}; cot x = \frac{1}{tan 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

sin^2\theta + cos^2\theta = 1

tan^2\theta + 1 = sec^2\theta

1 + cot^2\theta = cosec^2\theta

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/sec2a = sin2a . cos2a + cos4a

RHS = cos2a (sin2a + cos2a)

= cos2a (1) {we know, sin2a + cos2a =1}

= cos2a

LHS = 1/sec2a  = 1/(1/ cos2a) = cos2a

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 = \sqrt{5}/3
2. tan θ = 9/5
3. cos 23° + sin 25°
4. sec θ = 10/7

Why eTutorWorld ?

  • Learn at any time and from anywhere through unique personal lesson plans
  • Experience the extensive use of online resources and state-of-the-art technology
  • Enjoy one-on-one live personalized coaching
  • Navigate your homework with ease and learn advanced topics

Find out how eTutorWorld can help you improve your Grades.

No credit card is required, nor are you under any obligation to make a purchase. Just schedule the FREE TRIAL lesson to meet a tutor & get help on any topic you want!

Our Learning by Design methodology focuses exclusively on the individual student. Our tutors are specially trained to identify and diagnose the needs and interests of each student and plan lessons accordingly.

Find more about our Personalized Online Tutoring  Learning Packages.

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. Come to eTutorWorld for Expert Tutors and best K-12 Online Tutoring Services in the comfort and safety of your home at an affordable cost. Find a tutor online for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. Get free printable math and science worksheets in pdf format and SCAT Practice Tests. Sign up for a Free Trial Lesson Today!

© 2018 eTutorWorld - Online Tutoring and Test Prep | All rights reserved