The equation cos(θ + π/2) represents the cosine function of an angle (θ) added to π/2 radians. In other words, it is the cosine of an angle that is 90 degrees larger than θ.
To solve for θ, you can use a calculator or a trigonometric table to find the inverse sine (sin-1) of 3/7. This will give you the value of θ in radians. Alternatively, you can use the unit circle and the Pythagorean identity (sin2 θ + cos2 θ = 1) to solve for θ.
The relationship between sin θ and cos(θ + π/2) is based on the unit circle. As θ increases from 0 to π/2, sin θ increases while cos θ decreases. This means that when θ is added to π/2, sin θ becomes cos θ and vice versa. Therefore, cos(θ + π/2) is equivalent to -sin θ.
If sin θ is negative, it means that θ is in the third or fourth quadrant of the unit circle. In these quadrants, cos θ is also negative. Therefore, cos(θ + π/2) will be positive since it is equivalent to -sin θ. The exact value will depend on the magnitude of θ.
The equation cos(θ + π/2) is commonly used in physics and engineering to represent the phase difference between two oscillating systems. It can also be used in navigation and surveying to calculate the direction of an object relative to a reference point. In real-world scenarios, the values of θ and π/2 can be replaced with specific angles or measurements to solve for unknown quantities.