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Given that 6 cos θ + 8 sin θ ≡ R cos(θ + α) find the value of R - AQA - A-Level Maths Mechanics - Question 2 - 2020 - Paper 3

Question 2

Given that 6 cos θ + 8 sin θ ≡ R cos(θ + α) find the value of R. Circle your answer. 6 8 10 14

Worked Solution & Example Answer:Given that 6 cos θ + 8 sin θ ≡ R cos(θ + α) find the value of R - AQA - A-Level Maths Mechanics - Question 2 - 2020 - Paper 3

Step 1

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Answer

To find the value of R, we can compare the coefficients of the equation given:

[ R = \sqrt{(6^2 + 8^2)} ]

Calculating this:

[ R = \sqrt{36 + 64} = \sqrt{100} = 10 ]

Thus, the value of R is 10.

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