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## Applying Trigonometric Identities

#### High School - HSF-TF.B.5

How to Apply Trigonometric Identities - Identities are an expression or equation which are true. These identities can be trivially true for like x = x, or at times usefully true for Pythagorean theorems. You will find many trigonometric identities, but the common ones are: tan(x) = sin(x)/cos(x), cot(x) = cos(x)/sin(x), csc(x) = 1/sin(x), sec(x) = 1/cos(x), cot(x) = 1/tan(x), sin(x) = 1/csc(x), cos(x) = 1/sec(x), tan(x) = 1/cot(x), sin2(x) + cos2(x) = 1, cot2A +1 = csc2A, 1+tan2A = sec2A These trigonometric identities are applied in a number of problems. Follow the steps to apply trigonometric identities in a problem. 1. Convert all identities to cos. This can be done using the quotient and reciprocal identities. 2. Look at all the angles to find out the sum and differences and use appropriate identities to remove them.3. Remove the formulas appropriately and check for angle multiples.4. If you feel the need; expand the equations, combine the like terms, and then simplify. 5. If you find cos powers greater, replace them with sin powers using the Pythagorean identities.6. Cancel common factors after factoring numerators and denominators. 7. Now, check if both sides are equal or not. This collection of worksheets and lessons can be used to learn how to quickly simplify, prove, and solve trigonometric equations and expressions.

### Printable Worksheets And Lessons  #### Homework Sheets

The multiple choice version is what you will commonly see. That is why we highlighted it here.

• Homework 1 - Through every problem we need to remember the Pythagorean Theorem: a2 + b2 = c2 .
• Homework 2 - We need to remember the trigonometric relationship between tan and sin: tan x = sin x / cos x
• Homework 3 - tan x = a/b, cos x = b/c, sin x = a/c

#### Practice Worksheets

These are really order of operations worksheets with just a dash of geometry.

• Practice 1 - If tan x = 9, what is the value of sin x? Rounded to the two decimal places.
• Practice 2 - If tan β =24/12, then what is the value of cos β? Rounded to the nearest hundredth.
• Practice 3 - Use the values to confirm the output.

#### Math Skill Quizzes

Some choices can be discredited simply because you can't have the same answer twice.

• Quiz 1 - The reciprocal identities are pretty quick to learn.
• Quiz 2 - The negative angle identities can be used to get rid of negative angles.
• Quiz 3 - The sum of angles identities can help you break apart trig. functions.