We read your photo as:
Given that tan θ = (4)/(3). Find the value of sin θ - cos θ.
ScanSolve AI Answer
Step-by-step solution
4 stepsLet's solve question 6 from Section A.
Question 6: Given that tan θ = (4)/(3). Find the value of sin θ - cos θ.
Use the definition of tan θ to form a right-angled triangle.
tan θ = opposite / adjacent
Given tan θ = (4)/(3), we can consider the opposite side to be 4 units and the adjacent side to be 3 units.Calculate the hypotenuse using the Pythagorean theorem.
hypotenuse² = opposite² + adjacent²
hypotenuse² = 4² + 3²
hypotenuse² = 16 + 9
hypotenuse² = 25
hypotenuse = √25
hypotenuse = 5 unitsFind the values of sin θ and cos θ.
sin θ = opposite / hypotenuse = (4)/(5)
cos θ = adjacent / hypotenuse = (3)/(5)Calculate sin θ - cos θ.
sin θ - cos θ = (4)/(5) - (3)/(5)
sin θ - cos θ = (4 - 3)/(5)
sin θ - cos θ = (1)/(5)The value of sin θ - cos θ is (1)/(5).
Still stuck on this one?
Ask a follow-up, and the answer starts from this question.