10. f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 3
Question 10
10.
f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures.
g(x) = 2x - 3
(b) Find fg(34)
Give your answer correct to 3 ... show full transcript
Worked Solution & Example Answer:10. f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 3
Step 1
Find f(23)
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find f(23), we substitute x = 23 into the function f(x):
f(23)=4sin2(23)
Calculating sin(23) gives approximately 0.3907. Thus,
f(23)=4(0.3907)2≈4(0.1526)≈0.6104
Rounding to three significant figures, we obtain:
0.610
Step 2
Find fg(34)
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To solve fg(34), we first evaluate g(34):
g(34)=2(34)−3=68−3=65
Then we find f(65):
f(65)=4sin2(65)
Calculating sin(65) gives approximately 0.9063. Thus,
f(65)=4(0.9063)2≈4(0.8203)≈3.2812
Rounding to three significant figures gives us:
3.28
Step 3
Explain why.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The equation Ivan wrote, (x + 4)² = 25, contains a potential issue because it requires him to account for both the positive and negative square roots when solving for x.
The correct steps to solve (x + 4)² = 25 should include:
