Write the expression in terms of the appropriate cofunction.cot(25°)\cot\left(25\degree\right)cot(25°)

tan ⁡ ( 65 ° ) \tan\left(65\degree\right) tan ( 65° )

Write the expression in terms of the appropriate cofunction. cot ( 25 ° ) \cot\left(25\degree\right) cot ( 25° )

Welcome back, everyone. Let's try solving this problem. So here we are asked to write the expression in terms of the appropriate cofunction, and we are given the cotangent of 25 degrees. Now to solve this problem, our first step is going to be to find the appropriate cofunction for the cotangent, and that's going to just be the tangent. We learned this in the previous video. You can also recognize the names. Right? The cofunction for tangent would be cotangent, and so the cofunction for cotangent is just tangent. Now what we need to put inside the tangent is the complementary angle. And since I see our angle is measured in degrees, we're going to have 90 degrees minus the angle we started with, which is 25 degrees. That's always how you can find the complementary angle. So what I can do is subtract 25 from 90, and that's going to give me 65. So what we're gonna end up with is the tangent of 65 degrees, and that is the cofunction for the cotangent of 25 degrees. Hope you found this video helpful. Thanks for watching.

Write the expression in terms of the appropriate cofunction. cot ⁡ ( 25 ° ) \cot\left(25\degree\right) cot ( 25° )

tan ⁡ ( 65 ° ) \tan\left(65\degree\right) tan ( 65° )

tan ⁡ ( 25 ° ) \tan\left(25\degree\right) tan ( 25° )

cot ⁡ ( 65 ° ) \cot\left(65\degree\right) cot ( 65° )

cot ⁡ ( 25 ° ) \cot\left(25\degree\right) cot ( 25° )

2. Trigonometric Functions on Right Triangles

Cofunctions of Complementary Angles

Trigonometry

2. Trigonometric Functions on Right Triangles

Cofunctions of Complementary Angles

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Multiple Choice

Write the expression in terms of the appropriate cofunction.
$\cot\left(25\degree\right)$

$\tan\left(65\degree\right)$

$\tan\left(25\degree\right)$

$\cot\left(65\degree\right)$

$\cot\left(25\degree\right)$

Verified step by step guidance

Understand the concept of cofunctions: Cofunctions are pairs of trigonometric functions that are complementary, meaning they add up to 90 degrees. For example, sine and cosine are cofunctions, as are tangent and cotangent.

Identify the cofunction relationship: The cotangent function, $ \cot(\theta) $, is the cofunction of the tangent function, $ \tan(90° - \theta) $.

Apply the cofunction identity: Since $ \cot(\theta) = \tan(90° - \theta) $, we can rewrite $ \cot(25°) $ in terms of its cofunction.

Calculate the complementary angle: The complementary angle to 25° is 65°, because 90° - 25° = 65°.

Rewrite the expression: Using the cofunction identity, $ \cot(25°) $ can be expressed as $ \tan(65°) $.

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