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Example Questions
Example Question #81 : Trigonometric Identities
Which of the following trigonometric identities is INCORRECT?
Cosine and sine are not reciprocal functions.
and
Example Question #1 : Apply Basic And Definitional Identities
Using the trigonometric identities prove whether the following is valid:
Only in the range of:
Uncertain
True
False
Only in the range of:
True
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 #82 : Trigonometric Identities
Which of the following identities is incorrect?
The true identity is because cosine is an even function.
Example Question #83 : Trigonometric Identities
State in terms of sine and cosine.
The definition of tangent is sine divided by cosine.
Example Question #747 : Trigonometry
Simplify.
Using these basic identities:
we find the original expression to be
which simplifies to
.
Further simplifying:
The cosines cancel, giving us
Example Question #741 : Trigonometry
Which of the following is the best answer for ?
Write the Pythagorean identity.
Substract from both sides.
The other answers are incorrect.
Example Question #749 : Trigonometry
Express in terms of only sines and cosines.
The correct answer is . Begin by substituting
,
, and
. This gives us:
.
Example Question #750 : Trigonometry
Express in terms of only sines and cosines.
To solve this problem, use the identities ,
,
, and
. Then we get
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