High School Math : Trigonometric Identities

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Trigonometric Identities

Trig_id

What is the  of ?

Possible Answers:

Correct answer:

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: 

  

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Example Question #2 : Trigonometric Identities

Simplify .

Possible Answers:

Correct answer:

Explanation:

Simplifying trionometric expressions or identities often involves a little trial and error, so it's hard to come up with a strategy that works every time. A lot of times you have to try multiple strategies and see which one helps.

Often, if you have any form of    or  in an expression, it helps to rewrite it in terms of sine and cosine. In this problem, we can use the identities  and .

 

.

This doesn't seem to help a whole lot. However, we should recognize that  because of the Pythagorean identity .

We can cancel the  terms in the numerator and denominator.

.

 

Example Question #3 : Trigonometric Identities

Trig_id

What is the  of ?

Possible Answers:

Correct answer:

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

  

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Example Question #4 : Trigonometric Identities

Trig_id

What is the  of ?

Possible Answers:

Correct answer:

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

  

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Example Question #111 : Trigonometry

Simplify

Possible Answers:

Correct answer:

Explanation:

.  Thus: 

Example Question #2 : Using Pythagorean Identities

Simplify

Possible Answers:

Correct answer:

Explanation:

 

and

 .

Example Question #3 : Using Pythagorean Identities

Simplify .

Possible Answers:

Correct answer:

Explanation:

Remember that . We can rearrange this to simplify our given equation:

Example Question #4 : Using Pythagorean Identities

Simplify:

Possible Answers:

This is the most simplified version.

Correct answer:

Explanation:

Whenever you see a trigonometric function squared, start looking for a Pythagorean identity.

The two identities used in this problem are  and .

Substitute and solve.

Example Question #5 : Trigonometric Identities

Factor and simplify .

Possible Answers:

This is already it's most reduced form.

Correct answer:

Explanation:

To reduce , factor the numerator: 

Notice that we can cancel out a .

This leaves us with .

Example Question #1 : Trigonometric Identities

Simplify .

Possible Answers:

Correct answer:

Explanation:

To simplify , break them into their SOHCAHTOA parts:

.

Notice that the opposite's cancel out, leaving .

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