Answer:
cosine (90-θ) = sine (θ)
Cotangent (90 - θ) = tangent (θ)
Cosecant (90 - θ) = secant (θ)
Explanation:
The cofunction identities show the relationship between one function and its cofunction regarding complement angles.
Recall that the 3 pairs of cofunctions are:
- Sine and cosine
- Tangent and cotangent
- Secant and cosecant
The cofunction identity states that the value of a trigonometric function of an angle equals the value of the cofunction of the complement angle.
<u>(Remember that complement angles are two angles whose sum is 90)</u>
So if we have an angle θ, then the complement is 90 - θ (since θ + (90 - θ) = θ + 90 - θ = 90)
Thus we have that:
- cos (90-θ) = sin (θ) (sin is the cofunction of cos and θ is the complement of 90 - θ)
- Cotangent (90 - θ) = tangent (θ) (tangent is the cofunction of cotangent and θ is the complement of 90 - θ)
- Cosecant (90 - θ) = secant (θ) (secant is the cofunction of cosecant and θ is the complement of 90 - θ)
