A family travels 110 km East to spend the night in a hotel. The next day they drive back home, but after traveling 45 km West, they decide to stop and visit with friends for the night. Find the distance and displacement of the family.
Answer (3)
(cosx/sinx) + 5 =(cosx + 5sinx)/sinx;
When converting cotangent + 5 into ⅔/sin, you separate the cotangent term and the constant. The cotangent function is equivalent to the quotient of cosine over sine (⅔/sinθ), so when you add 5 to cotangent, it becomes (⅔/sinθ) + 5. You do not bring the 5 along with the ⅔ and sin within the same fraction. Instead, you keep the constant term separate from the trigonometric function.
An example of a trigonometric identity involving cosine and sine is: sin² θ + cos² θ = 1, which demonstrates the fundamental Pythagorean relationship between sine and cosine, often used when dealing with trigonometric expressions.
When converting cot ( x ) + 5 to cosine and sine, write it as s i n ( x ) c o s ( x ) + 5 . The constant +5 should be treated separately from the cotangent function. This keeps your mathematical expression clear and accurate.
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