Question

According to the cofunction​ identities, cosine (90 degrees minus theta )equals​_______, cotangent (90 degrees minus theta )equals​_______, and cosecant (90 degrees minus theta )equals​_______.

Answer 1

cosine (90-θ) = sine (θ)

Cotangent (90 - θ) = tangent (θ)

Cosecant (90 - θ) = secant (θ)

Step-by-step 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.

(Remember that complement angles are two angles whose sum is 90)

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:

1. cos (90-θ) = sin (θ) (sin is the cofunction of cos and θ is the complement of 90 - θ)
2. Cotangent (90 - θ) = tangent (θ) (tangent is the cofunction of cotangent and θ is the complement of 90 - θ)
3. Cosecant (90 - θ) = secant (θ) (secant is the cofunction of cosecant and θ is the complement of 90 - θ)