Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t. 
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
 
        
             
        
        
        
Answer:
B. eight fewer than a number
 
        
                    
             
        
        
        
Answer  
Given
Sean's house is currently worth $188,900. 
According to a realtor, house prices in Sean's neighborhood will increase by 4.8% every year.
To prove
Formula

Where r is the rate in the decimal form.
As given


               = 0.048
Put in the formula


 
        
   
Now also calculated monthly.
Formula

As given


               = 0.048
Put in the formula



As the approximation quarterly growth rate of the value of sean's house is near the Compounded quarterly interest .
Thus Option (A) is correct.
i.e
The expression  reveals the approximate quarterly growth rate of the value of Sean's house.
 reveals the approximate quarterly growth rate of the value of Sean's house.
 
                                                
                                                        
 
        
                    
             
        
        
        
Answer:
  - The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.
 - The scientist can substitute these measurements into  and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).
 and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).
Step-by-step explanation:
  You can observe in the figure attached that  "AC" is the distance between the Sun and the shooting star.
 Knowing the distance between the Earth and the Sun "y" and the angle x°,  the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.
  This is:
 
 In this case:
 
 Therefore, the scientist can substitute these measurements into  , and solve for the distance between the Sun and the shooting star "AC":
 , and solve for the distance between the Sun and the shooting star "AC":
 
 
 
        
                    
             
        
        
        
Inverse property is being shown