Questions: Use a cofunction identity to fill in the blank. cos(37°) = sin(□)°

Transcript text: Use a cofunction identity to fill in the blank. \[ \boldsymbol{\operatorname { c o s }}\left(37^{\circ}\right)=\boldsymbol{\operatorname { s i n }}(\square)^{\circ} \]

Solution

Solution Steps

To solve this problem, we need to use the cofunction identity for trigonometric functions. The cofunction identity states that the cosine of an angle is equal to the sine of its complement. In other words, \(\cos(37^\circ) = \sin(90^\circ - 37^\circ)\).

Solution Approach

Identify the given angle, which is \(37^\circ\).
Calculate the complement of the given angle by subtracting it from \(90^\circ\).
Use the cofunction identity to fill in the blank.

Step 1: Identify the Given Angle

The given angle is \( 37^\circ \).

Step 2: Calculate the Complement

To find the complement of the angle, we use the formula: \[ \text{Complement} = 90^\circ - 37^\circ = 53^\circ \]

Step 3: Apply the Cofunction Identity

According to the cofunction identity, we have: \[ \cos(37^\circ) = \sin(53^\circ) \]