Final answer:
To convert a cosine expression to its equivalent in terms of sine, use the Pythagorean identity to express cos(θ) as the square root of 1 - sin2(θ) or use co-function identities, ensuring to work in radians. Also double-angle can be used for certain expressions.
Step-by-step explanation:
To convert a cosine expression to its equivalent in terms of sine, especially in radians, one can utilize the Pythagorean identity which is Σ cos2(θ) + sin2(θ) = 1. Considering this identity, one can rewrite any cosine expression, for example, cos(θ), as the square root of 1 - sin2(θ), since cos2(θ) = 1 - sin2(θ).
Another method involves using the co-function identity where cos(θ) is equivalent to sin(π/2 - θ) or sin(90 degrees - θ in degree measure). Also, double-angle identities can be helpful, such as converting cos(2θ) into 1 - 2sin2(θ) or 2cos2(θ) - 1. Whenever applying these conversions, ensure that the angles are in radians for consistency in trigonometric expressions.
It's important to substitute the known values along with their units into the appropriate equation and check if the answer is reasonable. This process is vital for accurately converting and solving problems involving trigonometric expressions.