Questions: Find a cofunction with the same value as the given expression. sin 25° Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer. Type any angle measures in degrees. Do not include the degree symbol A. sin 25°=csc ° B. sin 25°=cos ° C. sin 25°=cot ° D. sin 25°=tan ° E. sin 25°=sec °

Find a cofunction with the same value as the given expression. sin 25° Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer. Type any angle measures in degrees. Do not include the degree symbol A. sin 25°=csc ° B. sin 25°=cos ° C. sin 25°=cot ° D. sin 25°=tan ° E. sin 25°=sec °
Transcript text: Find a cofunction with the same value as the given expression. \[ \sin 25^{\circ} \] Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer. Type any angle measures in degrees. Do not include the degree symbol A. $\boldsymbol{\operatorname { s i n }} 25^{\circ}=\mathbf{c s c}$ ${ }^{\circ}$ $\square$ B. $\sin 25^{\circ}=\cos$ $\square$ ${ }^{\circ}$ C. $\sin 25^{\circ}=\cot$ ${ }^{\circ}$ $\square$ D. $\sin 25^{\circ}=\tan$ $\square$ ${ }^{\circ}$ E. $\sin 25^{\circ}=\mathbf{s e c}$ $\square$ ${ }^{\circ}$
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Solution

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Solution Steps

Step 1: Recognize the Cofunction Identity

The cofunction identity relates the sine and cosine functions for an angle \(\theta\) in degrees as follows: \[\sin \theta = \cos(90^\circ - \theta)\] Given the trigonometric expression of the form \(\sin 25^\circ\), we use this identity to find its cofunction.

Step 2: Calculate the Equivalent Cosine Angle

To find the cofunction with the same value as \(\sin 25^\circ\), we calculate \(90^\circ - 25^\circ\). This gives us the equivalent cosine angle measure: \[90^\circ - 25^\circ = 65^\circ\] Rounded to 0 decimal places, the equivalent cosine angle measure is \(65^\circ\).

Final Answer:

The cofunction with the same value as \(\sin 25^\circ\) is \(\cos(65)^\circ\).

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