Processing math: 69%

Home / Aptitude Tests / Further Mathematics / Given that \(sin x =...

Given that $sin x = \frac{4}{5}$ and \(cos y = \frac{12}{1...

Given that $sin x = \frac{4}{5}$ and $cos y = \frac{12}{13}$ , where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).

A.

$\frac{63}{65}$

B.

$\frac{48}{65}$

C.

$\frac{56}{65}$

D.

$\frac{16}{65}$

View answer & explanation

Correct answer is A

$sin x = \frac{4}{5}$ and $cos y = \frac{12}{13}$

x is obtuse i.e sin x = + ve while cos x = + ve

$cos x=\frac{3}{5}==>cos x=-\frac {3}{5}(obtuse)$

$sin y= \frac{5}{13}$

$sin (x-y) = sin x$ $cos y - cos x$ $sin y$

$sin(x-y) = \frac{4}{5}\times\frac{12}{13}-(-\frac{3}{5})\times\frac{5}{13}$

$sin(x-y) = \frac{48}{65}-(-\frac{3}{13})$

$\therefore sin (x-y) = \frac{48}{65} + \frac{3}{13} = \frac{63}{65}$

See all Further Mathematics questions & answers

See more WAEC questions & answers

Similar Questions

Simplify $\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}}$ ....

A 35 N force acts on a body of mass 5 kg for 2 seconds. Calculate the change in momentum of the body...

Age in years 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 Frequency 6 8 14 10 12 ...

If $s = 3i - j$ and $t = 2i + 3j$ , find $(t - 3s).(t + 3s)$ ....

Find the unit vector in the direction of $-2i + 5j$ ....

In how many ways can the letters of the word 'ELECTIVE' be arranged? ...

In how many ways can the letters of the word MEMBER be arranged? ...

The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\...

The mean age of n men in a club is 50 years. Two men aged 55 and 63 years left the club, and the mea...

Evaluate $\log_{0.25} 8$ ...

Aptitude Tests

Typing Speed and Accuracy Test

Numerical Reasoning Questions and Answers

Quantitative Reasoning Questions and Answers

Spatial Reasoning Questions and Answers

Nigeria General Knowledge Questions and Answers

Puzzles Questions and Answers

Personality Test

Logical Reasoning Questions and Answers

Microsoft Office Questions and Answers

Abstract Reasoning Questions and Answers

Situational Judgement Questions and Answers

Verbal Reasoning Questions and Answers

Data Interpretation Questions and Answers

View latest jobs in Nigeria today