Square, Rectangle, and Parallelogram Problems, 13

Category: Plane Geometry, Trigonometry

"Published in Newark, California, USA"

From the given figure, find ∠A + ∠B + ∠C. 

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

Since the given figure is a rectangle that consists of three squares, then we can solve for the values of ∠A, ∠B, and ∠C by using basic trigonometric functions. The given diagonals are the hypotenuses of a square and two rectangles, respectively. 

The value of ∠C is
 

 

 

 

The value of ∠B is
 

 

 

 

The value of ∠A is
 

 

 

 

 

Therefore,
 

 

Solving Trigonometric Equations, 10

Category: Trigonometry

"Published in Vacaville, California, USA"

Solve for the value of x for the equation:

Solution:

Consider the given equation above

Since there's a half-angle function in the given equation, then we need to convert it into single angle function first as follows

Take the inverse cosine on both sides of the equation, we have 

                                     or

Therefore, the values of x are

 
where n is the number of revolutions. 
 

Solving Trigonometric Equations, 9

Category: Trigonometry

"Published in Vacaville, California, USA"

Solve for the value of x for the equation:

Solution:

Consider the given equation above 

Did you notice that all angles of the trigonometric functions are different? You can convert the multiple angles into single angles by the sum and difference of two angles formula but the equation will be more complicated. In this case, we will use the sum and product formula as follows

Take the inverse cosine on both sides of the equation, we have

                                                          or

Therefore, the values of x are

where n is the number of revolutions. 

Solving Trigonometric Equations, 8

Category: Trigonometry

"Published in Vacaville, California, USA"

Solve for the value of x for the equation:

Solution:

Consider the given equation above

Did you notice that the given equation consists of the product of trigonometric functions? Well, we have to split the product of trigonometric functions first into single trigonometric functions by using the sum and product formula as follows

Take the inverse cosine on both sides of the equation, we have

                            or

Therefore, the values of x are

where n is the number of revolutions.