+0  
 
+1
175
1
avatar+115 

1. Let \(A\) be an angle such that \(\tan(A)=\dfrac{1}{2}\). Find the value of \(\tan(A+120^{\circ})\), giving your answer in simplest radical form.

2. \(\cos \left(\frac\pi6 - \theta\right)\) can be expressed in the form \(A\sin \theta + B\cos\theta\) where \(A\) and \(B\) are constants. What is the value of \(\frac BA\)?

3. Consider angles \(x\) and \(y\) such that \(0 \le y \le x \le \frac\pi2\) and \(\sin(x+y) = 0.9\) while \(\sin(x-y) = 0.6\). What is the value of \((\sin x + \cos x)(\sin y + \cos y)\)?

4. Suppose \(\sin a + \cos b = -0.2\) while \(\sin b + \cos a = 1.6\). What is the value of \(\sin(a+b)\)?

 

Any help on these would be greatly appreciated! Thanks!

 Oct 19, 2019
 #1
avatar
0

1. tan(A + 120) = 4 - 2*sqrt(3)

 

2. A = sqrt(3) and B = 4, so A/B = sqrt(3)/4.

 

3. (sin x + cos x)(sin y + cos y) = 4/5.

 

4. sin(a + b) = 3/4.

 Apr 5, 2020

34 Online Users

avatar
avatar
avatar
avatar