Trigonometry : Apply Basic and Definitional Identities

Example Questions

Example Question #1 : Apply Basic And Definitional Identities

Which of the following trigonometric identities is INCORRECT?      Explanation:

Cosine and sine are not reciprocal functions. and Example Question #2 : Apply Basic And Definitional Identities

Using the trigonometric identities prove whether the following is valid: Only in the range of: Uncertain

Only in the range of: False

True

True

Explanation:

We begin with the left hand side of the equation and utilize basic trigonometric identities, beginning with converting the inverse functions to their corresponding base functions: Next we rewrite the fractional division in order to simplify the equation: In fractional division we multiply by the reciprocal as follows: If we reduce the fraction using basic identities we see that the equivalence is proven:  Example Question #3 : Apply Basic And Definitional Identities

Which of the following identities is incorrect?      Explanation:

The true identity is because cosine is an even function.

Example Question #4 : Apply Basic And Definitional Identities

State in terms of sine and cosine.      Explanation:

The definition of tangent is sine divided by cosine. Example Question #5 : Apply Basic And Definitional Identities

Simplify.       Explanation:

Using these basic identities:   we find the original expression to be which simplifies to .

Further simplifying: The cosines cancel, giving us Example Question #6 : Apply Basic And Definitional Identities

Which of the following is the best answer for ?      Explanation:

Write the Pythagorean identity. Substract from both sides. Example Question #7 : Apply Basic And Definitional Identities

Express in terms of only sines and cosines.      Explanation:

The correct answer is . Begin by substituting  , and . This gives us: .

Example Question #8 : Apply Basic And Definitional Identities

Express in terms of only sines and cosines.      Explanation:

To solve this problem, use the identities   , and . Then we get    