Question

Given: $\sin{A}= \frac{4}{5}$ and $\cos{B} = \frac{-5}{13}$; evaluate the following expression. (A: Quadrant I, B : Quadrant II.)?

 

 

1. $\sin{( A+ B )}$
2. $\cos{( A+ B )}$
3. $\sin{( A+ A )}$
4. $\cos{( A+ A )}$

Answer 1

Given sin A= 4/5 = O/H , using Pythagoras ,

b = √(5^2 - 4^2) = 3

cos B = -5/13 = A/H

         b = √(13^2 - 5^2) = 12

1. sin(A+B) , using compound angles

              = sinAcosB + cosAsinB

             = 4/5 x -5/13 + 3/5 x 12/13= 0.246... = 0.25

2. cos(A+B) = cosAcosB - sinAsinB

                   = 3/5 x -5/13 - 4/5 x 12/13 = -0.969... = -0.97

3. sin(A+A), using double angle,

              = sin2A = 2sinAcosA

                           = 2 x 4/5 x 3/5

                           = 0.96

4. cos(A+A) = cos2A = 1 - 2sin^A

                                 = 1 - 2 x (4/5)^2

                                   = -0.28